Thanks, Nick for vid #2 !
Now, I might seem a little OCD when it comes to your "K"-type element:

1) Realizing your ITC-100 has multi-choice possibility of element types:
"Support Multiple Thermocouples and Resistance Sensors (K, S, Wre, T, E, J, B, N, CU50, PT100)"
was the correct type chosen in its menu before startup?
And, if so - what's your take on the 800-ish deg top temp?
Did the element croak at 600 C, or was it still operative, pulsing the output to the SSR correctly?

2) Was the PID, per chance in a "J"-type factory setting - thus achieving the thermal runaway as I suggested previously?

Just curious after all these years - trying to learn, and avoid mistakes!

Small tip: Just adding an extra breaker (2-pole toggle, lo volt and amp) for the SSR pulse control,
to let the coils "cool off" a few secs before opening the door, might be a good idea for wire longevity.
Thermal shock isn't supposed to be something good for A-1, or any other wire type either.

Cheers
Johan