I'm giving this a like for backing up multiple users from the tty of the limping operating system. If you did that from the live .iso, it's equally adept footwork.
I have beat emergency mode twice (knock on wood) because my lightdm fell off. I couldn't rollback either due to that missing package stuff you mention (frustratingly). so remove dm and some other crap, reinstall, reboot. it took hours of trial and error and of course I never wrote it down.
Oh, yeah, the times I could not beat the OOPs or emergency mode greetings...I reinstalled🙂