Ok, we at least know the valid power detection / reset circuitry on the MPU board is not the problem.
And yeah, for whatever stupid reason TP1 and TP2 are opposite between Bally and Stern lamp driver boards
Something smells of these two problems being related to interrupt requests to/at the CPU. You've already changed the two PIA chips and the CPU which play a big part in this circuit. Until you get the meter we don't know if the 555 timer and zero crossing circuit on the board are working properly.
To prepare you when the meter arrives, set it to Hz, connect the black lead to ground and probing the red lead at:
Pin 40 of U11 (Display Interrupt generator input) should measure around 320Hz +/- 5%
Pin 18 of U10 (Zero Crossing detector input) should measure bang on 120Hz
Can you do one more thing for us. Measure the voltage on pin 18 of U11 of the MPU board. Then hook up the logic probe to the MPU board and put the probe on pin 18 of U11. Does the probe indication change when the game triggers a reboot? Let us know the results.