Never mind, fixed it :)
I think I'd crossed the streams while flailing at the options. The key is to add -gameio joy to emulators.cfg, so that it reads like this:lr-mess-apple2 = "/home/pi/RetroPie-Setup/scriptmodules/run_mess.sh /opt/retropie/emulators/retroarch/bin/retroarch /opt/retropie/libretrocores/lr-mess/mess_libretro.so /opt/retropie/configs/apple2/retroarch.cfg apple2e /home/pi/RetroPie/BIOS -gameio joy -flop1 %ROM%"
And then go into the MESS menu and set the analog controls up like this:
The key is those "P1 Joystick X Analog" and "P1 Joystick Y Analog" lines - you have to make sure those are set to "None", which isn't the default. Take those two steps and you should be sorted.