Problem solved here. What I had to do was unplug the keyboard dongle and reboot, then pair the joypads one at a time. With that done, putting the keyboard dongle back in didn't seem to conflict any more and everything's fine.
Contributions to the project are always appreciated, so if you would like to support us with a donation you can do so here.
Hosting provided by Mythic-Beasts. See the Hosting Information page for more information.