I don't know about stripping a body - I've done it several times, and I don't think I'd like to say one way or t'other whether the tone changed.
But I can say that stripping the lacquer off the back of a neck does indeed have an effect - much like you describe. I did it to a CIJ strat without taking the neck or strings off, not even bothered to detune it. Took a couple of hours, and the tone changed quite a lot (much to my surprise and, luckily, for the better :lol:). It became a more airy, more vibrant and "springy" sort of tone. This was good because I was trying to get more top-end out of it at the time, it sounds a bit woolly in comparison to my other strats.... Actually, the effect of stripping the back of the neck was MUCH greater than replacing the stock bridge assembly (zinc block etc) with steel stuff. However, it's still nowhere near as bright/airy as my Roadworns are.
I haven't stipped my Baja neck, and probably won't. I have considered stripping the body, but decided against it - I'd be worried about a slight reduction in size, that stuff looks well thick. I understand it is easy(ish) to do - apparently it comes off quite quick and cleanly with the heat-gun method.
Personally I'd go with Dave and say "replacement body" - Philly might have a good supply of them under his bed? (

:lol:)