@darksavior Just wanted to say thanks for the help. I don't know how I got myself so confused about the 2 drivers?
I uninstalled snesdev and tried again. It helped a little but the controller still wasn't working properly. The thing is, I'd left the wires I'd soldered on quite long, to make moving things around easier, and the wire I'd used wasn't of the best quality. I re-soldered a ribbon cable that was half the length of the old cable I'd used, connected it up as per the gamecon diagram, with just the gamecon driver installed and now everything's working.
Thanks for pointing me in the right direction.