Ok, so...
I have tried to install the proprietary driver via the Driver Manager in System Settings.
On reboot, SDDM presents a black screen on both monitors, plus the mouse cursor, and nothing else (or fails to load, leaving the black screen and cursor.). Can't log in.
I attempted the steps that fixed a similar problem in older versions of Kubuntu, but none of them did anything. (Example: "nomodeset" on the kernel line in GRUB. Blacklisting nouveau.)
I was unable to find a way back to Nouveau, so I re-installed.
I can't seem to find anything about the issue by searching on Google - plenty of similar issues for previous versions, but nothing that helps explain what I'm experiencing here - save for this bug report.
Any ideas?