Restore Messages using Time Machine (not iCloud synced)
OK I've tried a few different things, and I've got something that works. There are two key points:

You need to restore the whole Library/Messages folder (not just chat.db, as is said in most how-to's)
Before you do this, you need to close Message. But also, after you restore, you need to reboot the Mac.

Doing all of these things (close, restore whole folder, reboot) means that when you restart and open Messages, your backed-up version is present and functional.
Phew!