I ignored the laundry and the kitchen yesterday in favour of a lot of time on YouTube and a lot of staring at my spinning wheel, and ultimately decided to play around with where the drive band goes.
I went from the super huge not-remotely twisted fiber on the right to the intensely thin and twisty stuff on the left.
I did say it was twisty.
Having clarified the problem, I got all that mess off the bobbin, made a few more adjustments to the tension, and started again.
Well, maybe not perfect yet. But getting there!