I managed to fix it on my own soon after I posted this by figuring out how to rebind the controls on SNES9x2002; I'll share my steps for anyone else needing help with this.
First, load up any SNES rom on the most recent SNES9x LibRetro core. (This core runs crap on a Pi 0, but don't worry.)
Go into the Retroarch menu (Select + A or B, I can't remember) and go to the quick menu.
From the quick menu, go to controls and then rebind all the buttons for the controllers to how you want them.
Then save the core remap file.
Change your emulation core to SNES9x2002, and go back to the same control section in the quick menu.
Select 'Load Remap File" and navigate to the core remap file that was made for the modern SNES9x core and select it.
Finally, save the core remap file for SNES9x2002.
(All because we can't just do the first bit in SNES9x2002 for some reason... A pox upon you, whoever handled porting those old cores)
Oh, and some words to make sure this can be easily found by anyone who needs it:
SNES 9X 2002 remap rebind controls buttons GPi RecalBox PiSNES integer scale not saving sticking options settings
