I got the trace issue sorted - it wasn't supposed to go to that hole at all. I replaced the 7406 with no result (not that I really expected there to be). This is next to impossible without the schematics - so many different components can be traced back to the sync pins.
I'd shot gun them - there aren't that many - but one (the 74LS197) isn't available anymore except by NTE, and they want nearly ten bucks for it. I could probably source another Tetris PCB for only a little more than that.