And that problem, is now fixed without reinstallation.
I'm quickly becoming disenchanted with these people... so I'm not going to be feeding my (very hacky) workaround back at them, which was
to boot into the livecd, and copy across the old ldconfig.real (after a backup), and then go back into my normal session, check that ldconfig worked, run "dpkg --configure -a", and then reinstall libc for good measure. Everything seems to work now.
Not a fun experience.