If only I'd bothered to read further into some of the threads here.
I remembered reading that Acetone will strip off those HeroClix super-thick paint jobs.
I was very impressed initially. As soon as I dropped the Caped Crusader into the dip, I could see little sheets of that horrible blue paint fading away.
Then, we decided to go out for lunch, and I left Batman to his own devices.
I came home to find a cloudy blue mixture. I plunged in to find that not only had the paint all but disappeared, but his cape was badly mangled, and poor Batman was now a spongy mess. I dumped out the nasty acetone, and rinsed the Heroclix, only to realize one of his hands was now missing as well (most likely in the disposed acetone)
So, I in my ignorant haste have done what countless supervillians have failed to do.
The horrifying results:

