I have had something similar to this (not quite the same), I'd removed some connectors to get to an underside ramp and then put it back and not noticed one connector was one pin out when I put it back on. The coil just kept freezing in place when it was operated. Took me two hours to find what I'd done. Luckily no damage other than to pride.

Given your new info, that sounds very much less like a connector problem since I would expect that to effect every game. To isolate you could disconnect some coils and replay and see if the issue does or doesn't re-appear, hopefully narrowing down the field for you. Best of luck.

That now sounds much more related to cross board connection problems. No chance of a poor ribbon connection between boards? Even eprom poor leg contact?