Ok...after years of destroying little painted plastic pieces and settling for buying new ones, I did a little research into methods for stripping paint from plastic without damaging the plastic itself.
I turned to reading about painting and repainting model cars, since those guys have to deal with this problem quite regularly. As it turns out, there's a lot of methods, but most of them will change the appearance of the plastic and you'll have to re-coat it in the end anyways.
However, I did come across one product that eats paint but does not eat plastic (at least, not noticeably). It's Castrol Super Clean Degreaser. It's a clear purple liquid that chews through paint (and fingers, so be careful), but doesn't affect plastic. I went to home depot and bought some generic degreaser which contained the same chemicals. It just has to have the active ingredients as follows:
Sodium Hydroxide (Lye)
It cleaned a regular coat of paint off of submerged plastic parts in 4 hours, and a heavy coat of paint in 8 hours. Just make sure you wear gloves and eye protection when using this stuff. It's pretty nasty on your flesh. (ie: Lye eats skin) For heavy coats of paint, you can speed up the process by periodically scrubbing it gently with a soft toothbrush.