Aaaaand, I just found the answer.
In Calendar->Preferences->Acccounts, disable iCloud.
Then create a new calendar, giving it a name that doesn't conflict with any of the calendars in your iCloud.
Then re-enable the iCloud account.
The new calendar (under "On My Mac") remains.
Everything seems to be working normally from here on. I just need to move the relevant calendar contents back over from where they were put into iCloud, and re-publish these calendars. A bit of a pain, but at least I have a way forward.