I put "Ipac" in the diagram, didnt read your post properly

just to say where it was going to (I`m using a mini pac) , but the principle should be the same, INPUT one side of the switch and GROUND the other? you could wire (for example) the harness to "Player 1 Vert Button 1" then connect it from there (same side of the switch not through it) to "Player 1 Button 1 Horiz" effectively putting them in parrallel so both buttons trigger the same input.
you dont have to use all the 4 player inputs just ignore the player 3 and 4 ones (free`s up a load of inputs you could use for something else if an idea crops up, gawd knows what

errrr.. pinball buttons, volume , controls for a second screen jukebox/TV, other emulators), most mame games are two player and if you set up the defaults it`ll save you loads of time having to manually configure games.
Only player 1 controls mala, or rather only 1 input per option controls mala on that screen shot i posted, there may be another way of setting it up, but by wiring the inputs in parallel you`re basically making two Player 1`s at different seats and two player 2`s at the others (like the drawing). So you`ll be able to control it from the front or side as you wanted.
Only other thing i can suggest (with my VERY limited knowledge of mala and mame

) is if you have enough unused inputs make a mala control in reach of everyone, you just need up/down/left/right/start and exit .