Well, after two days work, scarily, I have two almost competently built baseboards. They are light strong and rigid. Built from 3/16" ply strips for the sides and 1/4" ply for the top. Glued and pinned.
I plan on adding a little extra bracing underneath. But at the moment it doesn't really feel like it needs it, to be honest.
The next step will be to add the blocks for the hinges so that the baseboards will fold over for storage and transport.