I've got a bunch of old 4:1 8pin mini din rotary switches (before I went with a SCART auto switch this is how I changed video input on my xRGB/OSSC).They are pretty cheap, I think I spent about 10$~15$ a pop.so technically it's 6 inputs (up, down, left, right, A, B) times 4 characters. Surely there's a rotary switch for the job? Mind you, it's probably not going to be a cheap part.
If you made all your controller heads 8pin, you could easily use this switch to change controls without fear of leaving active wires still connected.
I don't want to be a douchebag, but fuck it... Honestly this project is a really really bad/dumb idea.
I recommend you just abandon it in favor of the 2-player TMNT ROM that lets you select what Turtle you want to be at coin-up.