Thank you so much to everyone! It sounds like it's likely the RCT that's burnt out.
Ideally, I want to control the bottom coils, not a timer. If it's not too much trouble, is anyone able to explain how I would go about adding a third infinite switch? Would this allow me to control the relays for the bottom coils that are always closed/turned on?
According to the kiln theory manual, the only way to get "low" heat is by having the RCT cycle the coils on and off every 60 seconds.