So far no response to my query at the eGroupware forum. In the meantime, since I now know how to recover (thank you!), I've attempted the restore several more times. eGroupware isn't always broken the exact same way after each restore, but it is always broken in generally the same way -- e-mail never works, for example. Even in modules where the data seems to restore, the pages are littered with errors, the stylesheet is partly broken ... it's just a mess.
I guess I better start figuring out how to break the news to the boss ...