what are the numbers on the chips inside?If merely inverted, you can play make your own chip.
try drawing out the diagram, all the inputs from the JAMMA edge to that chip. The other pins will be power and outputs, you can trace those. The outputs should go into 74LS245s, 240s or 244s. The custom at the far end appears to be graphics, so methinks the inputs are running into TTLS, prolly the 20 pin ones alongside the dipswitches.
Basically, make an input RRC, a pullup 1K, a series 220 ohm and a 0.1 cap to ground. That goes for each invereter input, for each JAMMA input line. THEN the trick is to find out where they come OUT to....
Difficult but not impossible....
Good luck.