If anyone else has this problem, the cause was an extremely stubborn Mirror Image that would not and Would Not quit until it finally gave up.
Now that I have this lovely new backup and can run from it, how do I get safely out of here and back to the main drive so I can make a safety clone (assuming I can out-stubborn Mirror Image again)? Can I just click the Macintosh HD icon or do I need to do something more esoteric?