Found the issue, it was hard to see.
The larger ribbon cable has a cut in it across the first four traces caused by pulling against the metal clip.
That metal clip is an accident waiting to happen, it acts like a razor blade on the cable if there is any tension put on it.
I have another broken kss-220a with an intact cable, so I swapped it over and now it works about half the time I try to play a game. The pots on the cable were positioned slightly differently, so I moved the replacement into the position of the original (was this a bad idea).
I don't want to mess with any of the pots on the board.