Elbow Grease. Just about any chemical out there will affect the finish of the Plexi. Sanding, of course, will really do a number on it. I've had success in the past with a product by PollyS called Easy Lift Off. It's a paint stripper, but it hasn't affected the styrene kits I've used it on. It will remove enamels (especially the 1960's caked on enamel look that we did as kids to our Aurora monsters).
Spread a little on, let it sit overnight. The surface paint should wrinkle. Then use an old toothbrush dipped in the stuff to bruch the paint off. Since it's clear plex, I'm assuming it's somewhat flat. After you're done with that, you may have to go in with some very fine (like 10,000 grit) sandpaper and do a wet sand on the surface, followed by some plastic rubbing compound (also very fine), followed by some plastic polish.
That should restore it so it looks shiny, if not completely water clear.
Gene