I was a big MK fan back in the day and if I remember correctly, MK3 sort of forced you to use all 6 buttons. The first MK used start not to switch buttons but to block, if I remember correctly it was Street Fighter 2 where start swapped punches for kicks.
So starting with MK2, which in 1994 came at a time when everyone had the now-old 6 button controllers, I'm pretty sure it was just expected of the player. If not, it was definitely that way by Mortal Kombat 3 and especially UMK3. The latter came out in 1996, at the end of the Genesis' life, and used not 5 buttons like MK1 and 2 but all 6 with the Run button addition. By now the Nomad (handheld Genesis) had come out and also was built with 6 buttons.
In other words, unfortunately, this was one of the most button-demanding (and button combination-demanding) games to ever come out for the genesis, so by then it was sort of expected of people to have the 6 button controller. The game couldn't possibly be modified to only use 3 buttons, similar to the problem you're encountering now.
My advice would be to just remap the buttons in the game's config menu (there SHOULD be one). The GP32 does have 6 buttons, which I use comfortably for MK1 and 2 but haven't tried 3 or up (because START would have to be used for something, which is weird). My config is to use A for high punch, B for low kick, R for high kick, L for block, and select for low punch. With this I can capably play MK1 and 2 (for snes) but like I said i Haven't tried 3 or UMK3 yet because it's a lot faster than the other three games and uses an extra button. These two things combined seems like it would make the game pretty darn hard to play!
But good luck, I know what it's like to wanna get your MK fix.
EDIT: I realize that since I've been playing MK on opensnes, not drmd, the shoulder buttons and so forth may not even be available for drmd (which would correlate with what others were saying about drmd not supporting those buttons). If that's the case, then you may be screwed. I didn't know that drmd may not support those buttons at all, I do think that SHOULD be added myself.
