I can confirm that the Docker downgrade seems to work. I reverted my machine to a snapshot fresh after my own initial investigation and before @mpalmer had done anything, so nothing potentially useful should have been done at that point. I then stopped the app with ./launcher stop app, downgraded with apt-get install docker-ce=17.10.0~ce-0~ubunt, restarted the Docker service with service docker restart, and rebuilt my discourse instance to be safe with ./launcher rebuild app.
So far up and running for about an hour with no hitches, although there was an initially large amount of CPU usage that caused Discourse to chug while processing requests. I’m not sure what it was but figured it was the result of Discourse having been offline for more than a day (due to the snapshot timing). In any case, that subsided after about 10 or 15 minutes and all has been well since!
Big thanks @mpalmer for taking the time to look at our machine and find the problem! There’s no way we’d have a working forum at the moment without your help. 