Well everyone, it took a LOT of testing and redoing but we got it!
In the 5th pic down you can see the main power feed to the hot plate the breakers mount to was melted. This was the big clue that I didn't pick up on.
You can see the lug it screws into is cocked and not at a 90^ angle in relation to the hot plate.
Because this part is notched on the side (to butt up against the hot plate) being cocked meant that only the SCREW was transferring power between the wire and plate!
I took it all apart, put it back together properly, and tried it... but the breaker still popped.
Not to be discouraged I swapped the AC and Main breaker wires (to use the AC breaker for the mains) and guess what... it's been fine since!!!
So I think the excessive heat from the bad mains connection made the P120GF breaker pop too frequently and ruined it.
Only issue now? That breaker is $130 new! And no chance I'm getting a used one!
That can wait though... we don't need the AC till next year
So thank you everyone for all the suggestions and help!!!