The player 3 and 4 controls should just be wired directly to the game board(s). If you've got mutiple boards using those extra controls, you'll have to split them among all of the boards. I assume the common ground should be common among everything, so you'd probably just have to run the other wire from each switch to each of your three boards. It's the same thing I'll have to do with MK; I'll have to wire 2 buttons from each player directly to each of the three boards (and 3 on the MK3 board).
If that doesn't work, check that the grounds are all connected. On my cabinet, the various ground wires in the JAMMA connector were not electrically connected for some reason, so some controls didn't work with my JPAC. When I put all of the controls on a common ground, the JPAC liked them.
Since the cables are just supposed to be standard IDE cables, I assume they have 3 connectors because that's what they got cheapest...