OK, for anyone that reads this, here's what you need to know about fixing a softmodded Wii that was updated to 4.3E.
All I did was re-mod it as per the Mod ANY Wii post. Looks like the instructions have changed slightly since I did this - the bit where I had a problem have gone.
Anyway, I was fortunately to have bootmii in boot2, so I started with the "other desperate olptions" section. (Personally, I think that this is not at all desperate but a sensible place to start if you can!). I skipped part 2 (downgrading the system menu). The line "If MMM loads at boot, select Manage Priiloader, Edit Priiloader Hacks, enable needed hacks" in part 3 needs to be 3 lines higher in the instructions. I only read that after much messing around. D'oh!
That's it: no loss of save games. Job done.