Thank you for the references, Felix. Unfortunately, nothing you sent is applicable because SDDM doesn't even start in the first place. Computer goes unresponsive when it tries to start X and then I have to force shut down. I've been able to start - just - by booting into multi-user.target and masking KDE.unit from GRUB - apparently KDE ignores polite requests not to start up so you have to hide it from systemd entirely. I'll probably spend another tedious couple evenings trying to create log information before I have to force-off the system and then another wild goose chase finding the right package to blame only to discover about a week from now that the interaction between two or more unrelated packages is breaking my system - which is why I'm the only one with the problem.
Which makes me think that it would be great if there were some package rollback option where you can "apt-get undo" and reinstall the packages that were there before your system broke. But where's the fun in that?