There are two different version of C-Boards with kick harness connector, take a look to the picture. One of them with one 1×10 pins and the other one has 4+6+10+10 pins (the second version used with Capcom's Knights of the Round game, which can play also with 3 players!)
That second version you showed (90632C-6) is not used for Knights of the Round. I am aware of 4 different C-Boards which use at least one 10-pin aux. connector:
90628-C-2 (PPU2: B-12) (games: MERCS, ...)
90632C-1 (PPU2: many) (games: SFII, ...)
90632C-6 (PPU2: B-21) (games: SFII', ...)
90631C-5 (PPU2: B-21) (games: Captain Commando, Knights of the Round, King of Dragons, ...)
PPU2 is the big custom "picture processing unit" chip, is not necessarily the same across these C-Boards, and the game ROMs must be tailored to it. Though any A-Board will work with any game (ignoring 10Mhz vs 12Mhz clocks), the B & C Boards are fairly particular about how they are matched.
The only known Final Fight PPU2s are B-01, B-02, B-03, B-04, and B-05. Of those, the only potential match is some SFII World Warrior boards. In the photo you posted earlier with the Final Fight PCB running with SFII C-Board, you can see "B-05" on the chip. That's the only SFII PPU2 that could work with an original Final Fight game (and it must be a Final Fight that originally used a B-05 PPU2). Capcom used 9 different PPU2s for SFII World Warrior, so you can't just go buy a random SFII and expect it to have a B-05 PPU2 equipped C-Board for use with Final Fight.
@Grego, if you want to exchange some ideas on how to deal with this, I'm in the middle of a project that might dovetail nicely