I later had another attempt. I basically just ratchet-strapped the top of the ladders together so they couldn't go anywhere. And it worked! I had a platform! I now could do a much bigger part of the ceiling before I had to move my elevation device. Great! So I got steaming.
Some of the beams are difficult to get to, and you have to keep re-filling the steamer, and moving platform + sheet, and it's altogether a somewhat unpleasant job that smells and is hot and involves working above your head and dripping hot liquid on yourself but I made good progress. And one good Sunday it was done! That meant I would have to get mentally ready for sanding the bloody things too. After the scraping they don't yet look good enough to be varnished! Stay tuned...
The platform: a big improvement
Would the previous owner have smoked?