I've decided not pursue this further with support. The issue is getting enough airplay on a number of fronts. I'm glad I got my issue into Apple's tracking system and somewhat escalated, but I don't think it's worth my time to take it further.
It's easy to check the logs retroactively to figure out which files were locked when the backups failed. I use
For me, the files were in two places: ~/Library/Biome and ~/Library/Daemon Containers. I just excluded them from my backups and haven't had a problem since. I suppose if I left multiple users logged in, I'd have to do exclusions in more than one Library folder.
The exclusions cannot be made using the System Settings user interface; these particular directories cannot be selected. I set up the exclusions at the command line using the "tmutil" command. The man page is pretty clear on how to do it.
sudo tmutil addexclusion -p <some directory>