I nuked the TM drive this morning and created a new one, just as you suggested. Checkmate runs all kinds of tests on the drive (including surface scans, etc.) so I assume that the physical drive is OK. Sooner or later (hopefully sooner), I'll replace the drive with an SSD. For now, at least, all seems to be well. And yes, the drive is in a Thunderbolt enclosure.
For the record, one of the reasons why I nuked it was that, when I tried an experimental restore, I got the spinning beachball for several seconds before anything happened.
Jon
macOS 11.7.10, iMac Retina 5K 27-inch, late 2014, 3.5 GHz Intel Core i5, 1 TB fusion drive, 16 GB RAM, Epson SureColor P600, Photoshop CC, Lightroom CC, MS Office 365
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