I'd like to have a source of some nice gunk you can just dip the wire in and wipe off the insulation. Maybe I'm dreaming - in this post-EPA world...
Have you tried ordinary paint stripper? I have had various degrees of success with it. Depends on what kind of varnish they used. I seem to remember it working well with older wire, such as in repairing pre-WW2 audio transformers.
BTW, one of the things that makes many older transformers open up is the solder itlelf, that eats up the fine wire, the same process that causes your soldering gun tip to slowly disintegrate. The process is exacerbated by humidity. Some of the newer solders are not supposed to do that (don't know about the lead-free stuff).

