It appears we are functional again. First I rewired the short runs from the relay so the back plate could be off with everything connected. I plugged it in after and it powered up. Woohoo! Ya, not so fast... I moved all of the wires around to see if it would short out and it didn't. So, I started reattaching the back plate and the breaker disconnected. This made me think the power cord was kinked/ pinched and shorting where it is crimped entering the back plate so I pulled that section through the opening and cut back some outer jacket to inspect, but the wires were perfectly fine.
So, I replaced the PID controller Steve sent to test and it powered up again, but threw the breaker shortly after.
The only thing left was the heating element which I then replaced and so far that is working. It has been running without losing power for an hour at full power.
I am happy that it was possible to resolve without trying to safely ship the entire unit back. Fingers crossed it keeps working and I can finally cook this pastrami.