Ah, that didn't work so well.
Followed the steps at ollie-ries. Things locked up restarting LightDM. Took 3 reboots before LightDM showed up and I could log in. The launcher and the panel weren't there, but the two mouse cursors were.
When I removed and purged Mir, the system booted up into the low-resolution warning. Tried twice to reboot into recovery mode, but couldn't move the cursor or otherwise edit the Grub menu. Got there on the third reboot. Opened a shell and installed an Nvidia driver. Rebooted, into a high-resolution display of the low-resolution warning, and no mouse or keyboard.
C'est la vie. Think I'll wait. Off to reinstall.