I wouldn't worry about the -12V unregulated supply being a little lower than actually -12V. It is an unregulated voltage so anywhere from -12 to -14V or so is to be expected.

The positive 12V unregulated gets pulled down further than the negative since it is also supplying 5V. That is why they look so out of balance.

The voltage on the power supply is interesting, and looks good. However, what you really want to do is measure these voltages on CPU board. Between pin 14 and pin 28 on any of the ROM chips is a good place to measure.

Any battery damage on the board?

Anything above 5V on the actual CPU board is perfect. I don't think you have a power supply problem, especially considering you have a new power supply board.

You essentially reseated the ROM chips when you swapped boards from original to RD and back. Can you try reseating all the other socketed chips?

I think you should start looking for another board that might be dragging the 5V down (blowing the fuse in the original problem).

With the RD board, you get a new sound board, right? Maybe try disconnecting the sound board and aux sound overlay boards and seeing if the game will run without them. Some flashers and the disks will not work but you can see if it boots and restarts.

You said the 5V LED on the RD board was not lighting?

Agree, the whole problem could be caused by a flakey ribbon cables. I would replace them as the next step.

The 5V indicator on the CPU board is about as simple a circuit as you can get. It is just a resistor, LED tied to 5V. Since you measured 5V on the board, I suspect the LED or resistor has failed. Not very common but possible.

The volume is a good clue. The audio amps are driven by the 12V supply which is also used in the reset circuit. If the 12V supply sags, it is possible the reset circuit would restart the CPU. 12V enters the CPU board on J17 pin 9. 12V leaves the power supply board on J1 pins 11, 12, 13. Check these connectors for cold solder joints and bad connectors. Might be a good idea to replace the connectors at both these locations.

Since you are using your original power supply board again, have you replaced the header pins and replaced all the caps? Loosen and tighten the mounting screws on the 5V regulator (this mechanical connection is part of the electrical circuit). A cold solder joint somewhere on the power supply could cause a sag in 5V and/or 12V.

The aux driver board has minimal 5V chips, basically logic chips so it's really odd that this board would put you over the top on a healthy power supply. If it was that much of a draw, the 5V supply fuse should blow (do you have a properly sized fuse in the 5V circuit?).