I may just clean the old chain, relube it, measure it and reinstall it first, just to see if it works.
Yep, exactly that - a new freewheel will be installed later today.
This has never happened to me before. Because I want to learn more about this, I'm still going to make some measurements (comparative anatomy, as it were) and take some pictures for posting.
I may remove the cogs from the body, too, for closer inspection, flipping over and possible replacement.
It's a hobby, right, and you've given me lots of great ideas.