@matigo 90% my stupidity 10% sparsity of instructions from Apple.
In other news, turns out it is really, really complicated to copy the backups from an external hard drive to a Time Capsule. You can do external to external, and TC to TC, but external to TC requires a third party thing and lots of smarts.
It took me about three hours of useless searching to discover that.
So I'm just creating an entirely new backup, from scratch. Current extrapolation suggests that might take 83 hours, give or take.