Chad, I would not buy a new MPU as I don't suspect that is your issue.

Have you tried wiggling the power supply connections while the game is on? My guess is you are losing either power or ground from a loose connection or short. Can you post your voltages from the PS test points and maybe post a picture of 3J5 and 3J6 (top of PS board) from front and back. Did you repin any connectors on the PS? Verify that board is screwed in tight and the ground is good.

Someone above mentioned checking all your coil and switch diodes, did you get a chance to do this yet? It's always a good idea to do this I've had a broken diode cause all sorts of weird issues but never a total shutdown.

Intermittent issues are the worst; just when you think it's fixed..........

Also, can you clarify if the flippers are now NOT working during the shutoff? Looks like you posted the opposite previously

Re-pinning is different than replacing capacitors. Post a picture of the solder joints along the edge of the back of the power supply board, the male connectors on that board, and female connectors that connect to them.

If it was me I would just redo them anyway. Watch a TNT video and he talks about reflowing and re-pinning on every game they touch

Voltages while the game is on (meter on VDC, red on test point, black on ground braid)
Wiggle cables while the game is on, being careful not to touch anything other than the cable you are trying to move.

Did you guys make any progress? Its going to be next to impossible to find an intermittent problem by just playing the game then looking after it locks up.