Follow-up for anyone else in my situation:
Once I transferred my UNRAID registration to a new USB key, I assigned my drives to their previous locations and started the array and all my docker containers started up like normal. But I couldn't update any of them as they did not have config files. I proceeded to back-up my appdata folder first, then I re-added the docker apps from Community Apps plugin and they all installed-in-place, and created the necessary config files. I had to force the update on one of them, but the rest updated through the Docker section. Rather painless overall.