Magnolia Mud Research

Probably. 
Part of the fun of working with found materials is the variability. Sometimes close enough is all that’s needed.

I make terra sig regularly with my local clay and follow something similar to @Magnolia Mud Research’s post. I don’t go to great lengths to extract any remaining “finest particles” from the dregs. I played with that a bit but found it was counterproductive.  Letting it slake a few hours then mixing it really well gets the all good stuff in suspension. 
I’m sure this is derived from Vince Pitelka or maybe Pete Pinnell, but it’s what I go with:
1 quart water to 1 pound of clay. 2.5 grams deflocculant per pound of clay.
My deflocculant is half soda ash/half sodium silicate. 

At 800 degrees, the glaze particles have not begun to sinter, they are just a little toasty. Fix the kiln and refire.

Your not alone there.
White is just about the first adjective I think of when bone china is mentioned. It's an interesting idea that it might really be objectively bluish but subjectively  "whiter than white" (like many detergents).

The change from "whiter than white" to a more visible greenish tint then doesn't seem so implausible. Possibly due to some subtle change in the nature of the glass in which the (iron?) chromophore is embedded.
From @Min's reference.

PS a test-tile without Veegum seems an increasingly interesting idea.
BTW how are small test-tiles for different body compositions usually made? Using volumetric mixing ideas from glaze tests would seem sensible if you need to do lots. Perhaps drying the over-wet samples on plaster or in plaster moulds - or applying as a slip to a biscuit tile (although that might make inspection more difficult).
PPS Can you confirm that you have observed the green tint under several different lighting conditions. So we can exclude any light-spectrum related issues (c.f. neodymium glass).

The two photos are from Luxurybonechina.com and narumi.co.jp. 
A link to another photo is here: https://simple.wikipedia.org/wiki/Porcelain#/media/File:Transparent_porcelain.jpg
I get the sense a greenish tinge to bone china is not so unusual. The green of the piece @Jarman Porcelain posted is tilted away from a yellowish I would expect from iron, but not so much to make me think iron’s not primarily responsible. The clay body is a hair’s breadth from being a glaze at maturity (the ultimate clay/glaze interface: the pot is the glaze). Grolleg and Standard both have over 0.5% iron in them, perhaps that’s enough to show when it’s all in the melt? NZK has half the iron of those two, so I don’t know.
I found this interesting, since I feel like I hardly know what I’m talking about: https://www.jonsinger.org/jossresearch/tjiirrs/017.html
I certainly imagine getting some into a reduction firing, being able to compare, would provide useful information. 

Do you think there is a link between the Veegum  and the bone ash or TCP? (Veegum being magnesium aluminum silicate) Interesting read here https://www.researchgate.net/figure/Concentrations-of-phosphorus-pentoxide-and-magnesia-in-Roman-emerald-green_fig1_277089354 possibly linking the two with a green colour.

I've been there.  and learned to ignore the "official methods" and simply crushed the dry clay as small as possible using a hammer and kitchen screen utensils to get rid of the "big" rocks.  
Mix the clay with water to make a slurry that is somewhere between the buttermilk and the milk level (or a little less).  Let the mixture set for a while to let the heavy particles to sink, and then pour the liquid into a separate container which will contain most of the sig.  Stir up the original container again and let it set a while, and repeat pouring off the water to get remaining sig. Yes, this is not the official method, but it has worked just fine for the clay I take from my ponds and roads to them.  I have also used that same method for making sig from scrap commerical clay bodies. 
If you are able to get wet clay from the backyard just start with that; add water and mix well; if you have sand, it will sink along with the heavy particles.  I have a pond that collects fine clay every time there is a decent rain. After the rain there will be a thin layer of fine clay above the big paricles.  My first round on terra-sigillata I followed the "official" method; it worked ok.  After noting what was happening in the ponds and just getting a bucket of pond mud and water I begin to make my own method which has worked just as good as the textbook. 
The best "official" recipe I have found (beyond my own) is Vince Pitelka's version:
http://www.vincepitelka.com/wp-content/uploads/2022/10/Super-Refined-Terra-Sig.pdf   
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I've been there.  and learned to ignore the "official methods" and simply crushed the dry clay as small as possible using a hammer and kitchen screen utensils to get rid of the "big" rocks.  
Mix the clay with water to make a slurry that is somewhere between the buttermilk and the milk level (or a little less).  Let the mixture set for a while to let the heavy particles to sink, and then pour the liquid into a separate container which will contain most of the sig.  Stir up the original container again and let it set a while, and repeat pouring off the water to get remaining sig. Yes, this is not the official method, but it has worked just fine for the clay I take from my ponds and roads to them.  I have also used that same method for making sig from scrap commerical clay bodies. 
If you are able to get wet clay from the backyard just start with that; add water and mix well; if you have sand, it will sink along with the heavy particles.  I have a pond that collects fine clay every time there is a decent rain. After the rain there will be a thin layer of fine clay above the big paricles.  My first round on terra-sigillata I followed the "official" method; it worked ok.  After noting what was happening in the ponds and just getting a bucket of pond mud and water I begin to make my own method which has worked just as good as the textbook. 
The best "official" recipe I have found (beyond my own) is Vince Pitelka's version:
http://www.vincepitelka.com/wp-content/uploads/2022/10/Super-Refined-Terra-Sig.pdf   
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Cobalt being v expensive I wonder if your glaze could handle less. 2% seems a high amount of cobalt oxide.
 

I use a plastic bowl for water . Its a wide open form -I keep a cut shammy on the lip and few sponges in it. I get fresh warm water every throwing day from electric tea kettle-my guess is 1/2 +gallon of water-less water the better in terms of throwing

Some time ago I posted about challenges with wollastonite clumping.  I have now found a process which is helping with this issue.  I utilize one of these flour sifters when weighing out the wollastonite.
  I sift the material directly into a pan on the balance until I have the necessary amount.  It's pretty low tech, but it works.  Perhaps not feasible for large-scale batches, but I'm usually making 1-2kg batches of most of my glazes, and it works fine for that.
 

I would make my own wash and remove with a wet sponge  before firing any commercial wash as it usually poor quality.
Speaking of quailty wash I noticed on the Advancer shelve (kiln shelve.com ) site they use the same formula as I posted years ago
1/2 alumina hydrate
1/4 epk
1/4 calcined EPK or (glowmax)

when wondering around the property this week I notice a rotting stomp of a large pine tree that was blown down a few years ago; the dried yellow clay still on the bottom of the stomp was simular to the color of the plastic cat litter buckets;  the clay on the stump contains iron oxides.  Long ago while solving problems for plastics, fine particles of iron oxides were used to produce colors to the plastics.  
My point is you should think about the iron being taken from the plastic.  Test using a plastic bucket that is not yellow.  
LT

when wondering around the property this week I notice a rotting stomp of a large pine tree that was blown down a few years ago; the dried yellow clay still on the bottom of the stomp was simular to the color of the plastic cat litter buckets;  the clay on the stump contains iron oxides.  Long ago while solving problems for plastics, fine particles of iron oxides were used to produce colors to the plastics.  
My point is you should think about the iron being taken from the plastic.  Test using a plastic bucket that is not yellow.  
LT

Hi and welcome! I wish it was under better circumstances.
The pictures are worth a thousand words, and thank you so much for including those!
The fact that the piece is broken so cleanly, and in 2 near-perfect vertical lines all the way through means that this wasn’t specifically your clay, or anything you did during building the piece. It’s a nice dense clay  that probably stuck to the kiln shelf due to the mass and size of the piece, and cracked during cooling. For the next pieces, I’d fire them on some sand/alumina so that the piece has the equivalent of little refractory ball bearings to shift around on. You could also use a waster slab that will shrink at the same rate as the piece, but take the brunt of the force and absorb the crack instead.
If the clay survived the bisque just fine, another possibility is to not fire the piece to full clay maturity. Porosity in the end piece is less of a concern for you than it would be for someone throwing functional ware.

quit using crimp connectors and get the better clamp ones from Euclids-If you had the clamps you only need a short wire to get it to clamp. I have extra insulators so I would grind one down on my bench grinder and that would expose enough pitail to clean and clamp and on with the show. Creative fix is needed.

This is a great point I've never considered that, I'll try warming my pieces up in the future and see what happens. Thank you!

 
 
I'll read through this, thank you for sharing!

 
 
Yeah, I would like the coloring to last as long as possible. 10 years is pretty long but permanent is ideal. I'll give the china paints and luster a shot and see what happens.  Thanks for all the info and such a detailed reply!
 

It's easier to overpower these little round kilns. Sometimes you need to back off the burners to get them to go. Also, what size shelves did you have in the kiln? You usually need to use a smaller shelf than what an electric kiln of that size would use, so there's room for air to flow. A lot of people also put a shelf at the top, like 3 inches below the flue opening. Even a short pipe over the flue will increase the draw. You can even make a small chimney out of stacked soft brick.

You need a damper-I suggets thin broken kiln shelve say 1/2 inch thick so that the weight is minimal -or just a soft brick which is light still
Also I would run as the larger pipe (I thought you said it was 3/4) all the way to kiln. It looks like you necked it down somewhere in last 10 feet with smaller flex? Its usually not a pressure issue with natural gas its a volume issue, so keep the pipe as big as you can to the kiln.
I have those same type of burners on an updraft .  You cannot change your altitude  so you need to have all the other functions perfect 
 

If the mixture is homogenous, the shrinkage rates should wind up somewhere in between the 2 different points. You’re making a whole new clay body.

Another thing you can do to toughen up unfired glazed pots is spray them with laundry starch. (the aerosol kind, not the spritzer bottle)

Google searches on Japanese pottery throwing methods do bring up quite a bit of information. You may find some Utube videos that will help you also. Years ago, I was having problems with S cracks in the bottom of small vessels off of the hump.  . a utube video showed me to make a pancake on the hump and then bring up the sides and then pull the walls. This was a Japanese method.
 
 
best,
Pres

You could empty the mixer and let the bottom dry out and get it out that way and rehydrate it again in small pieces.
welcome to tne forum

Welcome to the forum!
Unfortunately, the chimney isn't going to work. It may be the correct size, but the heat is going to destroy it in no time, and it'll likely be glowing orange outside the kiln.  You also need a damper in it, and because you're using venturi burners it's probably far too short to provide the secondary air needed for combustion. I highly recommend looking at a kiln design book like Frederick Olsen's 'The Kiln Book'. It's a somewhat outdated but it's got some solid design work in it and it's really about the best we have. It'll give you the calculations needed for flue opening dimensions and chimney height. Your chimney needs to be built from firebrick to at least the height of the kiln, and then you could transition to metal after that if needed, but it's often easier to just keep with brick.
Where will the kiln be located while firing?
What is the BTU rating of your burners?
How thick are the walls, and what type of insulation is behind the bricks?

The 2 inch is best -more insulation is always better
If that rod is subject to lots of heat I would use stainless steel as it will not corrode  like steel does, if its a low heat (well insulated around it mild steel is fine. My guess is, it got hot and flue gasses made it corrode  to dust. now if you are going to fire kiln on a hobby basis then steel will last fine ,but if its a kiln that will be used all the time stainless is worth the cost. Thicker steel hold up longer than thinner steel
These use factors play a big part in how well things hold up.