@Shakz will try...
Edit: Aha, there seems to ONLY be an issue with the N64 emulator. I had mapped by triggers and shoulder buttons wrong, so that is fixed now. It works on all emulators but the N64 one - which is unfortunate considering that's the one I use the most.
Edit 2: It works now?! It just doesn't display the text that indicates that a save state has been saved / loaded / selected! There is still the fact that Majora's Mask lags when NPCs are in the area, but that's something I can live with for now. Thank you for your help!