no, the rubber membrane, I think I messed my gamecube one up, you could feel it was a lot "looser" than the other 3 buttons. Mine ended up using a NES controller's board and rubber membrane with a gameboy color d-pad.
-try it with the lid off with the membrane on. is it still oversensitive?
-look at the inside of the lid, make sure there's nothing holding the dpad up a little, like some stray plastic from grinding.