Certainly worth the time to plow through all this, but I didn't find an answer to my specific situation. I think I discovered what triggered the issue, however. I changed the scheme on my machine to use iCloud to become the primary document storage for this two-user machine (two users, two separate logins, etc.). It looks like Time Machine is tripping up over files that once resided in the machine but have now been punted over to iCloud. I was successful is creating a new backup destination on my original AirPort Time Capsule, so far at least (creating the new backup is going to take about 18 hours or so). But at least that'll give me some reassurance that I have backed up the M2 Mini before I start experimenting with finding out what files that Time Machine is choking on, and why. Maybe.