PeterH

This might help
It’s important to go the correct speed in the last 100c of the firing to achieve the expected heatwork, so whether worn elements, not enough power, stuck relay,, anything that extends the last 100c will have a dramatic effect. Prior speed, not so much. 

Are you sure that this isn't an indirect  reference to heat-work? Perhaps in the context of unachievable ramp speeds.

A year late to this, but I experimented with carbon process back in the 70s, both with Hanfstaengl black carbon tissue and with self-made materials.  I had some success in placing gelatin/pigment images on glass, that showed some promise of at least limited continuous tone density range.  I used glass because Kodak glass slide covers were readily available and accepted coatings.  I used one or another hardness of photo gelatin, and dry pigments from the art store. 
(I have had good results in ceramics with selected Gamblin dry pigments: Cr green, Co blue, Fe/Mn umbers and siennas, as dry press body colorants and in hot oil intaglio transfer inks.) 
Recall that in continuous tone carbon, your range of image density is created by range of pigmented film thickness, the image will harden from the exposure lamp side inwards, and that you need ultraviolet (I used a now-contraband 60s suntan mercury vapor suntan bulb).  You are running a race between colorant density needed to form the image, and colorant+frit... density absorbing and scattering the exposure light against hardening more of the carrier.
It's tempting to try this again, but I feel that it is no longer responsible to flush dichromate, even where it might not be directly illegal.  Oh yeah: also the formaldehyde for hardening.  Diazos aren't necessarily super safe, but at least they're easy to destroy.

Funnily enough, @ThruTraffic’s inspo image is from Bandanna Pottery’s instagram, one of the links Peter posted about.  I recognized it right off, but if you’re ever wondering about the provenance of an image, reverse image search is a pretty fun toy.
So good news! That clay is already in your back yard, no orders from overseas necessary. They’ve got their process described in the link Peter posted. If you don’t want to dig your own, I’d check out Highwater’s catalog, and look at adjusting one of their bodies. They might even have something that’s already what you’re looking for.
Because I’ve been following Naomi Dagliesh and her husband for a few years now, I know the clay is pretty short, and she cuts those feet with the edge of a wooden rib. It leaves the grit they add to the clay exposed. They get that texture only partly from the material: technique is significant as well. 

Personally I doubt it's practical, but this at least tells you not to overheat it (see the last sentence in the quote).
Might be worth a try in a domestic oven.
https://en.wikipedia.org/wiki/Plaster
Chemistry
See also: Calcium sulfate § Hydration and dehydration reactions Gypsum plaster, gypsum powder, or plaster of Paris, is produced by heating gypsum to about 120–180 °C (248–356 °F) in a kiln:[18][13]
  CaSO 4 ⋅ 2 H 2 O ⟶ heat CaSO 4 ⋅ 1 2 H 2 O + 1 1 2 H 2 O ↑ {\displaystyle {\ce {CaSO4.2H2O {\overset {heat}{{}->{}}}{CaSO4.1/2H2O}+ 1\!1/2 H2O ^}}} (released as steam). Plaster of Paris has a remarkable property of setting into a hard mass on wetting with water.
CaSO4⋅12H2O+112H2O⟶CaSO4⋅2H2O{\displaystyle {\ce {CaSO4.1/2H2O + 1 1/2H2O -> CaSO4.2H2O}}} Plaster of Paris is stored in moisture-proof containers, because the presence of moisture can cause slow setting of plaster of Paris by bringing about its hydration, which will make it useless after some time.[19]
When the dry plaster powder is mixed with water, it rehydrates over time into gypsum. The setting of plaster slurry starts about 10 minutes after mixing and is complete in about 45 minutes. The setting of plaster of Paris is accompanied by a slight expansion of volume. It is used in making casts for statues, toys, and more.[19] The initial matrix consists mostly of orthorhombic crystals: the kinetic product. Over the next 72 hours, the rhombic crystals give way to an interlocking mass of monoclinic crystal needles, and the plaster increases in hardness and strength.[20] If plaster or gypsum is heated to between 130 °C (266 °F) and 180 °C (350°F), hemihydrate is formed, which will also re-form as gypsum if mixed with water.[21][22]
On heating to 180 °C (350°F), the nearly water-free form, called γ-anhydrite (CaSO4·nH2O where n = 0 to 0.05) is produced. γ-Anhydrite reacts slowly with water to return to the dihydrate state, a property exploited in some commercial desiccants. On heating above 250 °C (480°F), the completely anhydrous form called β-anhydrite or dead burned plaster is formed.[19][22]
 

Personally I doubt it's practical, but this at least tells you not to overheat it (see the last sentence in the quote).
Might be worth a try in a domestic oven.
https://en.wikipedia.org/wiki/Plaster
Chemistry
See also: Calcium sulfate § Hydration and dehydration reactions Gypsum plaster, gypsum powder, or plaster of Paris, is produced by heating gypsum to about 120–180 °C (248–356 °F) in a kiln:[18][13]
  CaSO 4 ⋅ 2 H 2 O ⟶ heat CaSO 4 ⋅ 1 2 H 2 O + 1 1 2 H 2 O ↑ {\displaystyle {\ce {CaSO4.2H2O {\overset {heat}{{}->{}}}{CaSO4.1/2H2O}+ 1\!1/2 H2O ^}}} (released as steam). Plaster of Paris has a remarkable property of setting into a hard mass on wetting with water.
CaSO4⋅12H2O+112H2O⟶CaSO4⋅2H2O{\displaystyle {\ce {CaSO4.1/2H2O + 1 1/2H2O -> CaSO4.2H2O}}} Plaster of Paris is stored in moisture-proof containers, because the presence of moisture can cause slow setting of plaster of Paris by bringing about its hydration, which will make it useless after some time.[19]
When the dry plaster powder is mixed with water, it rehydrates over time into gypsum. The setting of plaster slurry starts about 10 minutes after mixing and is complete in about 45 minutes. The setting of plaster of Paris is accompanied by a slight expansion of volume. It is used in making casts for statues, toys, and more.[19] The initial matrix consists mostly of orthorhombic crystals: the kinetic product. Over the next 72 hours, the rhombic crystals give way to an interlocking mass of monoclinic crystal needles, and the plaster increases in hardness and strength.[20] If plaster or gypsum is heated to between 130 °C (266 °F) and 180 °C (350°F), hemihydrate is formed, which will also re-form as gypsum if mixed with water.[21][22]
On heating to 180 °C (350°F), the nearly water-free form, called γ-anhydrite (CaSO4·nH2O where n = 0 to 0.05) is produced. γ-Anhydrite reacts slowly with water to return to the dihydrate state, a property exploited in some commercial desiccants. On heating above 250 °C (480°F), the completely anhydrous form called β-anhydrite or dead burned plaster is formed.[19][22]
 

It sounds like you’re using commercial dry mix, correct?
The only thing to be mindful about storing glazes outdoors in the heat is evaporation. Check your consistency and maybe measure your SG before each glazing session to make sure the consistency is where you want it. This should be done anyways, but life does happen. 
More issues happen with cold. I had an unheated garage studio for a long time. Freezing glazes isn’t the end of the world, but it does make dipping glazes hard pan. You can rescue them, just be prepared for it to take a while, and you’ll absolutely need to re-sieve. As long as the plastic container they’re in is still flexible and there’s room for ice expansion, even those will survive. Continued cold under the freezing mark can make plastics brittle, but I think that’s not going to be an issue for you in San Francisco Bay Area. 
A note about the article that Peter linked: if you have some solubles in your glaze, you might want to be more mindful of the temperature if you aren’t using your glaze for months at a time. You can tell if your glaze has solubles if the water that rises to the top of the bucket is not clear. If the temperature gets to about 15*c (59F) or lower, over the course of a month or so, glazes with either soluble boron and calcium, or lithium can start to form assorted solids. The lithium ones will be flat-ish, and have an octagonal or hexagonal shape. Those can be re-dissolved in hot water and added back into your glaze so you’re not changing any chemistry. Boron/calcium ones will be little round guys. I have yet to find a method of re-dissolving them. If you’ve only got a few of the borocalcium ones, they can be discarded without too much damage, but be sure to use up the full batch before adding any more ingredients to your bucket. If you remove too many, you can affect your glaze’s chemistry. 

You could prevent the mould by adding a biocide. Short lived ones (that require topping up) are hydrogen peroxide and bleach (but bleach may be hard on the hands). A long-lived one is copper carbonate. 
The Best Way to Eliminate Odor from a Stinky Ceramic Slop or Glaze Bucket
- Try to make sure that your waste doesn't get near any aquatic life, especially if you use a long-lived biocide.
- I could understand your "wild" clay going mouldy if it has lots of organics in it, but am surprised that shop-bought bentonite does.

You may find this of interest

How to Increase or Reduce Crazing in a Glaze
How to Adjust Crackle Without Changing the Overall Appearance of the Glaze
https://ceramicartsnetwork.org/daily/article/How-to-Increase-or-Reduce-Crazing-in-a-Glaze

I find terra sigillata a confusing term, which is also often unrewarding to use in searches. Some of the issues are described in
Terra sigillata https://en.wikipedia.org/wiki/Terra_sigillata
 
The introduction is especially relevant, and I include the first paragraph of it.
Terra sigillata is a term with at least three distinct meanings: as a description of medieval medicinal earth; in archaeology, as a general term for some of the fine red Ancient Roman pottery with glossy surface slips made in specific areas of the Roman Empire; and more recently, as a description of a contemporary studio pottery technique supposedly inspired by ancient pottery. Usually roughly translated as 'sealed earth', the meaning of 'terra sigillata' is 'clay bearing little images' (Latin sigilla), not 'clay with a sealed (impervious) surface'. The archaeological term is applied, however, to plain-surfaced pots as well as those decorated with figures in relief.

I find terra sigillata a confusing term, which is also often unrewarding to use in searches. Some of the issues are described in
Terra sigillata https://en.wikipedia.org/wiki/Terra_sigillata
 
The introduction is especially relevant, and I include the first paragraph of it.
Terra sigillata is a term with at least three distinct meanings: as a description of medieval medicinal earth; in archaeology, as a general term for some of the fine red Ancient Roman pottery with glossy surface slips made in specific areas of the Roman Empire; and more recently, as a description of a contemporary studio pottery technique supposedly inspired by ancient pottery. Usually roughly translated as 'sealed earth', the meaning of 'terra sigillata' is 'clay bearing little images' (Latin sigilla), not 'clay with a sealed (impervious) surface'. The archaeological term is applied, however, to plain-surfaced pots as well as those decorated with figures in relief.

If you heat air from 0°C to 1000°C it expands to less than five times its size. [It goes from 273°K to 1273°K and expands to 1273/273 its size.]

Water expands by about 1700 times when it turns into steam (over a much shorter temperature range). at's a lot.

After some searching I found this paper. Which contains some though-provoking facts and ideas.
Recovery and Revival of Attic Vase Decoration Techniques
What can they offer archaeological research ?
https://tinyurl.com/yecn6xnf

Of course the firing (and final effect) of this "black gloss" is different from that of t-sig, but they both start by forming a "colloidal slip" (with or without the use of a deflocculant).

p114 Gives the results of  X-ray analysis of historic samples and modern "reproductions"
- This clearly shows that the originals didn't use phosphorous-based deflocculants  (many reproductions used calgol).
- The "glaze" contains much lower calcium levels than the body.
118 It is pointed out that
- The absence of phosphorous in the glaze implies that  plant-ash deflocculants weren't used.
- Although not conclusive the potassium levels suggest that potash defloculants weren't used either.
 p119  Looking for a deflocculant-free method of producing the "colloidal slip".
- Using a low-calcium clay (similar to that used in antiquity) they found that they could get acceptable (deflocculated?) results a pH>8.7 and >15°C.
- Using the same clay pre-soaked for six months they got similar (not-deflocculated?) results at pH~7 and >15°C.
... this suggests that slip production was a seasonal process, probably during the warmer spring to autumn.
... assisted by over-winter soaking of the clay.
The difference in calcium content between different clays is shown in fig2




PS I couldn't help speculating:
1. That the need for low-calcium clay was because that any soluble calcium compounds would act as deflocculants. After all soluble calcium and magnesium compounds  are used a deflocculants for glaze slips.
2. Historically they may have found suitable candidate clays simply by paddling round the local clay-pits in late spring, looking for signs of spontaneous colloidal dispersion.  Those wishing to find suitable modern commercial clays may need to look at them after a 6-months soak.

Or just go on long walks. Makes sense.  According to my ceramic history class, a lot of Roman era potting in Europe was a seasonal, part time gig. You did it when you weren’t busy farming, and there’d be time to source and prepare materials in advance. 

After some searching I found this paper. Which contains some though-provoking facts and ideas.
Recovery and Revival of Attic Vase Decoration Techniques
What can they offer archaeological research ?
https://tinyurl.com/yecn6xnf

Of course the firing (and final effect) of this "black gloss" is different from that of t-sig, but they both start by forming a "colloidal slip" (with or without the use of a deflocculant).

p114 Gives the results of  X-ray analysis of historic samples and modern "reproductions"
- This clearly shows that the originals didn't use phosphorous-based deflocculants  (many reproductions used calgol).
- The "glaze" contains much lower calcium levels than the body.
118 It is pointed out that
- The absence of phosphorous in the glaze implies that  plant-ash deflocculants weren't used.
- Although not conclusive the potassium levels suggest that potash defloculants weren't used either.
 p119  Looking for a deflocculant-free method of producing the "colloidal slip".
- Using a low-calcium clay (similar to that used in antiquity) they found that they could get acceptable (deflocculated?) results a pH>8.7 and >15°C.
- Using the same clay pre-soaked for six months they got similar (not-deflocculated?) results at pH~7 and >15°C.
... this suggests that slip production was a seasonal process, probably during the warmer spring to autumn.
... assisted by over-winter soaking of the clay.
The difference in calcium content between different clays is shown in fig2




PS I couldn't help speculating:
1. That the need for low-calcium clay was because that any soluble calcium compounds would act as deflocculants. After all soluble calcium and magnesium compounds  are used a deflocculants for glaze slips.
2. Historically they may have found suitable candidate clays simply by paddling round the local clay-pits in late spring, looking for signs of spontaneous colloidal dispersion.  Those wishing to find suitable modern commercial clays may need to look at them after a 6-months soak.

After some searching I found this paper. Which contains some though-provoking facts and ideas.
Recovery and Revival of Attic Vase Decoration Techniques
What can they offer archaeological research ?
https://tinyurl.com/yecn6xnf

Of course the firing (and final effect) of this "black gloss" is different from that of t-sig, but they both start by forming a "colloidal slip" (with or without the use of a deflocculant).

p114 Gives the results of  X-ray analysis of historic samples and modern "reproductions"
- This clearly shows that the originals didn't use phosphorous-based deflocculants  (many reproductions used calgol).
- The "glaze" contains much lower calcium levels than the body.
118 It is pointed out that
- The absence of phosphorous in the glaze implies that  plant-ash deflocculants weren't used.
- Although not conclusive the potassium levels suggest that potash defloculants weren't used either.
 p119  Looking for a deflocculant-free method of producing the "colloidal slip".
- Using a low-calcium clay (similar to that used in antiquity) they found that they could get acceptable (deflocculated?) results a pH>8.7 and >15°C.
- Using the same clay pre-soaked for six months they got similar (not-deflocculated?) results at pH~7 and >15°C.
... this suggests that slip production was a seasonal process, probably during the warmer spring to autumn.
... assisted by over-winter soaking of the clay.
The difference in calcium content between different clays is shown in fig2




PS I couldn't help speculating:
1. That the need for low-calcium clay was because that any soluble calcium compounds would act as deflocculants. After all soluble calcium and magnesium compounds  are used a deflocculants for glaze slips.
2. Historically they may have found suitable candidate clays simply by paddling round the local clay-pits in late spring, looking for signs of spontaneous colloidal dispersion.  Those wishing to find suitable modern commercial clays may need to look at them after a 6-months soak.

If you heat air from 0°C to 1000°C it expands to less than five times its size. [It goes from 273°K to 1273°K and expands to 1273/273 its size.]

Water expands by about 1700 times when it turns into steam (over a much shorter temperature range). at's a lot.

After some searching I found this paper. Which contains some though-provoking facts and ideas.
Recovery and Revival of Attic Vase Decoration Techniques
What can they offer archaeological research ?
https://tinyurl.com/yecn6xnf

Of course the firing (and final effect) of this "black gloss" is different from that of t-sig, but they both start by forming a "colloidal slip" (with or without the use of a deflocculant).

p114 Gives the results of  X-ray analysis of historic samples and modern "reproductions"
- This clearly shows that the originals didn't use phosphorous-based deflocculants  (many reproductions used calgol).
- The "glaze" contains much lower calcium levels than the body.
118 It is pointed out that
- The absence of phosphorous in the glaze implies that  plant-ash deflocculants weren't used.
- Although not conclusive the potassium levels suggest that potash defloculants weren't used either.
 p119  Looking for a deflocculant-free method of producing the "colloidal slip".
- Using a low-calcium clay (similar to that used in antiquity) they found that they could get acceptable (deflocculated?) results a pH>8.7 and >15°C.
- Using the same clay pre-soaked for six months they got similar (not-deflocculated?) results at pH~7 and >15°C.
... this suggests that slip production was a seasonal process, probably during the warmer spring to autumn.
... assisted by over-winter soaking of the clay.
The difference in calcium content between different clays is shown in fig2




PS I couldn't help speculating:
1. That the need for low-calcium clay was because that any soluble calcium compounds would act as deflocculants. After all soluble calcium and magnesium compounds  are used a deflocculants for glaze slips.
2. Historically they may have found suitable candidate clays simply by paddling round the local clay-pits in late spring, looking for signs of spontaneous colloidal dispersion.  Those wishing to find suitable modern commercial clays may need to look at them after a 6-months soak.

@ThruTraffic some catholic priests used to wear an itchy shirt made of horsehair as penance, so they’d be forgiven for their sins. That’s the cole’s notes version, but enough for your own google search. Saying something is hair shirt is saying that it’s unnecessarily uncomfortable/painful/difficult.

Apologies to all, a real senior moment.

If you heat air from 0°C to 1000°C it expands to less than five times its size. [It goes from 273°K to 1273°K and expands to 1273/273 its size.]

Water expands by about 1700 times when it turns into steam (over a much shorter temperature range). at's a lot.

If you heat air from 0°C to 1000°C it expands to less than five times its size. [It goes from 273°K to 1273°K and expands to 1273/273 its size.]

Water expands by about 1700 times when it turns into steam (over a much shorter temperature range). at's a lot.

You may find this of interest, especially the sections What is Heatwork?  and  Put Witness Cones in Every Firing.
Temperature vs Heatwork – Why We Use Witness Cones
https://suemcleodceramics.com/do-you-put-witness-cones-in-every-firing/

The pottery shop most associated with this process is Dock 6. Kerry Brooks is the potter and she applied this process to coasters as well. She spent a year, or two, developing the process and the glazes that go with it. 
Again, she spent a year, OR TWO, developing this and I know she had a lot of failures. (Her studio/shop is a few miles from mine. I know she experimented with glazes, with firing temperatures, and with types of glass.)
Once she found success technically she found success in the marketplace. (Anthroplogie ordered 1000's.) 
Having seen failed experiments with coke bottles, in high school and college, I have never felt inclined to attempt anything like this. She found the sweet spot and her coasters really are a thing of beauty.

Thinks for posting the kiln plate. I hope that the experts will chime in, but I suspect that the max temperature of 1300C means that the element life - when firing to your desired temperature -- is likely to be quite short.
For example see the first answer in
PS I'm not certain if the figure of 50 firings includes the lower-temperature bisque firings.