Okay - some updates.
I'm experiencing two different resets, both of which are outlined in the article that Kkuoppamaki shared. One is with the lights blinking, with which LED204, blinks and L2 stays on - and one where the game goes to black and starts up again with only L2 on when the game goes down.
schudel5 - when I went to reseat them, they did exactly as you had said, fell apart in my hand.
However - something to note, when the game is operating, it's acting strangely. It hasn't operated enough in a while for me to notice anything until I stress tested it today. Scoring weird points, DMD occasionally lags or gets stuck.
Please also refer to this thread I made -- https://pinside.com/pinball/forum/topic/how-bad-i-ruin-my-game-please-help-stern-monopoly#post-4451244
It was resetting the same way before that thread.
My way of going about this at this point:
Reflow solder on boards.
Then if needed,
Replace connections mentioned by schudel5
Then if needed,
Put in new game rom.
Is that the right way to do this?