Well, blow me down.
I ran a manual Time Machine backup on Sunday – about 16GB – and it ran without a hitch. No error messages, no stopping. Progress, of a sort, though I have no idea why it suddenly decided to start working again. (Note that I have granted this unholy amalgam of silicon and software independence and agency. I am in its power.)
I have set the iMac to back up to Backblaze every night. I use the Amphetamine app to keep the iMac awake for 10 hours after I go to bed. As of today, about 24,000+ files and 441MB of data still to be uploaded.
I have not plugged in and installed the external drive yet. But there is no hurry. With up-to-date Time Machine and Crashplan backups, and the Backblaze experiment going well, I feel reasonably secure. Creating an additional local backup has a lower priority right now.
I feel more urgency to step away from this computer for a while, rest up, and let it do its thing.