I think some of those 4 player games could be set up in their DIP switches to allow for a smaller coin door. i.e. you would insert coins into any coin slot, then press a corresponding start button for the player you were using... or maybe I misunderstood those options I dunno.
You could set the player Start buttons to be coin buttons instead, in TMNT and X-Men and Simpsons, since those games only had player coin slots and the two player buttons, no individual start buttons. Or you could set those games to free play. You can also get two really thin individual coin slots, and install them to either side of the door you bought... I think I priced that once and found that the cost-per-slot was pretty even across the different numbers of slots you could get, at least on Happ's site.