I'd be really wary about using any sort of 
chemical/solvent anywhere near a cel... because 
it might actually affect the acetate itself, not 
just the paint. So I'm not sure what to 
suggestion about removing that nasty tape goo. :( 

As far as acid-free tape goes, you OUGHT to be 
able to find it anyplace that has framing 
supplies and photo book supplies. You might have 
to try more then one of that type of store 
though. In the framing section you'll probably 
find a fiber-based tape that is acid free and is 
pretty wide and VERY adhesive. But in the photo 
book section you might be able to find good old 
Magic Tape. They do make an acid free variety. 

You'll have to judge if you think you can safely 
remove all that tape or not. If you do, when you 
reframe the cel, only put a little bit of tape 
across the top corners to adhere it to the mat. 
The tape should cut across the corner diagonally. 
You can also put a little piece of tape across 
the top in just the middle, but from what I 
understand, its best to only do it on the 
corners. Acetate is kind of a living, breathing 
thing, that will change its shape somewhat, so if 
the entire top of it is taped down, you might get 
some warping. 

Hope this helps!