Just throw the model in with the base on it and get some new bases.

I wouldn't use brake fluid, since it will be too slow. Look for aerosol "brake parks cleaner". It is faster, a convenient spray, and just as toxic. It also melts plastic. I've used it before (and the can said 'Made in China', but might be for export only.

Brake parts cleaner is pretty common, available in places like Walmart here. If you can't find it look for a paint stripper at an auto parts store.