Warning you are about to go down the rabbit hole!
Simplest approach would probably be an off the shelf solution to just hack in a x box with controllers and be done with it.
You've suggested several hardware hacks. If you really wanted to dedicate the effort you should be able to retain the original controls but then you will fight with the game software/emulators to get the type of control and feedback you are after. (Take a peek at the racing simulator world for other control hacks, mostly PC centric)
You didn't mention what games you are most interested in or linking the cabinets (who wouldn't). I would suggest a game driven approach (pick the games you are most interested in and follow the "best" path to that experience based on what others have done).
I think the Atari & Williams cabinets have similar Happs Steering in them & 5K pedal pots? I think those are both 4:3 25/27" monitors (keeping or replacing monitors? Almost certainly easier to replace than to interface depending on your approach).
As much as I appreciate MAME I think it is a poor choice for most racing games that I enjoy, but then again I don't understand which racing games you are after.
68hc11