Having adjusted the polygon it now works. It seems that the problem was that the polygon crossed the antimeridian (180E/W).
Another issue is that whenever you edit (add or move a point) a polygon the map is zoomed out to show the whole polygon, so (if you're doing fine changes to the boundary) you keep having to zoom back in. (A different class of bug - a user-hostile interface rather than the failing functionality described in the first paragraph.)
Addendum: after creating a project with the polygon crossing the antimeridian, and then changing the polygon, the project ended up in an odd state where it wasn't linking property. (HREFs from the forum 404ed, and the project was omitted from the latest projects list.) The project had been deleted and a replacement created.