Thanks for that thorough reply Grangur. So I need to sand until smooth, but not sand until all paint removed, right? The reason I'm thinking of respraying is that I though it would be easier than going down to bare wood (which I would prefer, to be honest, even on the ply bass). I live in a flat with no workshop or garage, and no sanding tool or heat gun or anything. And I'm a cheapskate.
Maybe it's not such a great idea. Hmm. Or buy a heat gun and go at the bodies with that and a load of sandpaper, then finish with Danish oil.
I will think on.