Wouldn't it also be a good idea to test the voltage of the power supply. Arn't they ajustable? If so It might be crankes up and that might explain the burning.
High or excessive voltage does not cause burnt edge connectors. Poor terminal contact due to loose fitting terminals or tarnished contacts create resistance. Current flow across resistance generates heat. This heat burns the edge connector. So no, voltage is not the an issue here.
There are a couple of different methods to repair an edge connector. If this board is going to be in a typical Jamma rig where you might be swapping boards out on occasion, and need to unplug and reconnect the board from time to time, I'd highly suggest one of the fingerboard methods. Anything else (such as foil repairs) won't hold up long to repeated unplugging and plugging back in.
Bob Roberts has a nice writeup about one way to do a fingerboard, plus he stocks the parts to do it:
Read here: http://www.therealbobroberts.net/pace.html
Don't forget to replace the terminals in the harness connector when you repair the board, they are likely as damaged as your board edge!
Also, like Lutus mentioned, it's not a bad idea to trace the coin door light feed and see if it is daisy chained to the Jamma connector. It's not uncommon to find them wired like that. In cases like this I will often move the coin door light feed right to the switching power supply, either +5 or +12, depending on which bulbs you have or want to use (like 555 will use +5 and 194's use +12). It's not something you need to do if you have good connections, but that current, small amount that it is, doesn't need to be on the Jamma connector, so moving it right to the switcher will lighten the load on the edge connector a little.
D