Genboomxer

The last 200F degrees are all that matter in terms of heatwork/cones and your glazes. Prior to that, you really just want a program that your pots can handle, and that your kiln can keep up with. My kilns can only maintain 325F/hr up to about 1950ish and still maintain evenness before it lags. But that's plenty fast. I do a simple 3 step program going up:
200F/hr to 200F, hold as needed
300F/hr to 1975F
100F/hr to 2175F
That gets me to cone 6 in about 8.5 hours. It's a schedule my kiln can keep up with even with heavy loads.  I do the same ramps for bisque.
I don't think there's any reason to add a hold midway up. If things are going to even out, they should do it in the last 200F degrees. With single zone kilns, how you load it is going to have a huge effect on how evenly it fires, probably more than the firing schedule. Pack the center tight, pack the top and bottom lighter.

I wondered about that too, but I double checked and it's there.  I can copy this schedule and remove the hold. 
However, like many kilns, mine fires unevenly and a hold somewhere in the process evens things out.  Maybe add a 5 min hold  at the beginning of the cool ramp (1900º)?
P.S. - I triple checked.  Turns out I was cocky at some point and took it out of Novice Mode and added the 15 min hold.  
Learning every day... 

Interesting. How would the 350F/hr ramp affect the next segment, 150F/hr slowing, and why should that matter if the final ramp up is the more important? 
The 500F/hr was a paste error. I ran the schedule with 9999.  
Confirmed set to type K.  Also, I found the Genesis tech manual.  I'm now armed and dangerous.

I just looked at the med/slow cone fire program and the schedule is:
120F/hr | 180; 120/hr | 250; 300F/hr | 1000; 150F/hr | 1100; 180F/hr | 1982; and final ramp is 108F/hr | 2232F with a 15 min hold, then a similar cool down to what I've been using.
Looks very gradual with a 2-step  'candle'.  I may skip the first segment since I usually wait a day or 3 for glazes to dry completely. 
I'll know in a couple weeks how it works out.
I happen to have an infrared. Thanks for the tip!  Prior to the last 3 firings I replaced the 6-30 plug because the old one got hot and melty around the prongs. I've basically overhauled this little kiln!  I'm probably expecting it to do more than it can. 
My education and experience continue. 
Thanks again!!!

Interesting. How would the 350F/hr ramp affect the next segment, 150F/hr slowing, and why should that matter if the final ramp up is the more important? 
The 500F/hr was a paste error. I ran the schedule with 9999.  
Confirmed set to type K.  Also, I found the Genesis tech manual.  I'm now armed and dangerous.

Nice work, easy to give up. Way to stick with it! Hopefully you are all set.

I win!
Full power test gives hot elements, and seems like it's heating faster than the last time I did the test. If that's possible.
Hopefully this means an end to E1 codes.
Thank you for the expert help and patience, and for making me a lot smarter. 
 

Yep, looks good.

I don't think we need to be looking at the Cress relay setup at all. The elements run on 240 volts, so just connect the element connection wires to the Electrositter accordingly. 

Hmm, I need a better way to do this. This should be your relay including the numbers. The wire on terminal 6, connects to the wire on terminal 8. The wire on terminal 2 connects to the wire on terminal 4. You should be able to take a picture and include the numbers which would allow us to confirm. You are only jumping out this relay so the elements are powered all the time your controller sends power to the kiln. The relay in the controller will cycle everything on and off as it needs to. I am assuming your kiln is wired into the controller.
The middle elements are powered by the top infinite switch. If you have jumped H2 to L2 and H1 to L1 on that switche then you have jumped out that switch as well. Whenever power is applied to the kiln all elements will come on full. Again pictures would help confirm.
To add - finally noticed your drawing link. The bottom two connections on this relay cycle this relay on and off. The top infinite switch cycles this relay when turning on the middle elements. You can disconnect and insulate so this relay doesn’t keep firing after it’s jumped out.

 

You won't have to do anything inside the controller. It already has a 50 amp relay wired to the four screws on the back of the Electrositter. All you need to do is wire the power cord to the correct 2 terminals on the Electrositter, which you've already done, and wire the elements directly to the other two screws. You'll just have to make sure the elements are wired correctly. I don't see a wiring diagram for that specific model on the Cress website, but there are several that are probably similar, and it looks like the top and bottom elements are wired in series, and the middle elements are wired in series? If that's the case in your kiln, then piece of cake- one lead wire from the t/b and one lead wire from the middle will connect to one screw on the Electrositter, and the other two leads will connect to the other screw.

Good news - I finished bypassing all the switches and it cleaned up the panel quite a bit.  I double checked the routing and connections; taped off the exposed terminals, etc.  Turned it on and, voilà, nothing went Zzzzot! I calibrated the TC (again) and did a full power test. The relay clicked, the pilot light went on, control panel read 'FIRING'.
Bad news -   Cold elements.
I opened it again and rechecked wiring. Rinse/repeat; nothing...
I'm too tired and disappointed at the moment to go back in tonight. I'm sure I missed something simple. I did notice the relay click was not as snappy and loud, so maybe it was on the edge of failure and my pulling and pushing on the terminals did it in. I ordered a new relay because the ones I have on hand aren't the correct spec.
The definition of 'experience' is when you didn't achieve what you wanted in the first place.  At least I'm getting experience.
Any suggestions for how to troubleshoot this is greatly appreciated.

I'm in the process of doing that right now.  It doesn't seem too complicated and it looks like I can repurpose most of the wires too.  Stay tuned...

knowing that, 
I guess I would jump out all the connections of the infinite switches with good solid connections, including the magnecraft relay and disconnect the timer - no use for it running.

No, you may be perfectly correct but if either of the infinite switches do not go full on or their internal contacts have any voltage drop including the relay, things become random. The thumb wheel timer is powered in the off cycle of the magnecraft relay and the on cycle of the lower infinite switch which mechanically affects the top infinite switch. Way too much stuff and connections for me. Now that you have a real controller everything goes and I install my own 12vdc relays controlled by the Genesis. One for element set 1 and one for element set 2..  The loading on each is approximately 12 amps which is light. Mount them in as cool a location as practical and they last a long time. The sitter can stay as a safety or eventually be jumped when you have confidence in the controller. Since these are graded elements you should operate as a single zone.
IMO:  too many items to depend on acting correctly, too many connections. If you have a controller no need to have all the extra complication.
The Genesis controller only has outputs for 12vdc at low current so it does need relays to function. And is also powered by a 12/24 ac center tapped transformer so I am not clear on how you have that wired. Other than a 12 vdc replacement relay for the old 240 vac magnecraft. If so, is the timer connected to the NC contacts of the new 12vdc relay? I think I just upgrade this to how modern kilns work and simplify it.

Sorry saw this earlier and just could get back to it now.
Looking at the schematic of this, I would suggest you remove the thumb wheel and infinite switch(s) and replace with relays. I believe that is causing your random results. If I read the specs correctly your kiln was 24 amps and a 30 amp breaker and minimum #10 gauge wire was suggested.
Diagram I found FTX23 and FX23f. https://cressmfg.wpenginepowered.com/wp-content/uploads/FX23F-FTX23-220.pdf
Could not find FX23P though.

60 amp circuit? Shouldn't that be 30 amps?
Assuming the thermocouple is good, the only other thing I would expect is a relay that's sticking when the kiln gets hot. I'd start with changing the thermocouple, though.
At 18" wide and 22.5" deep, and pulling 24 amps, I'd say that kiln is not a very strong cone 10 kiln, more like maybe cone 8/9. But it should still get to cone 6 with the elements in spec.
I would change that rate to 9999/hr.  At 500/hr you're in the realm where we often see problems because the kiln can't cool that quickly.