When a Playfield is told to "look like" another morph it becomes a SketchMorph. I'd expect it to just change its appeareance. That is, it should change its sticky background morph to look like that other Morph. This would be consistent with the fact that I can just paint on it via the halo, which actually paints onto the background morph.
I'm not quite sure where to hook into, so no fix yet.
-- Bert