Okay, so it turns out I misremembered a few things. I checked my old laptop, and it seems I stopped using ePSXe because I couldn't use my USB joystick properly. Old versions of PCSX-R had trouble too, but apparently I got it to work on that emulator eventually. So I got it wrong; I didn't change the input plugin on ePSXe (though I did for PCSX-R).
Anyway, if you have to use ePSXe, you can get around the keyboard issue by using a program that translates joystick input into keyboard strokes. QJoypad is a good one, however, I found Rejoystick to be a better solution (does not rely on Qt, just SDL and X11).
Anyway, if you have to use ePSXe, you can get around the keyboard issue by using a program that translates joystick input into keyboard strokes. QJoypad is a good one, however, I found Rejoystick to be a better solution (does not rely on Qt, just SDL and X11).