I had to deal with this problem on my 96 Galant after the headlights got to the point they were just about not visible anymore.
I didn't want a temporary solution--I wanted permanent. So what I finally found that worked was a kit made for aircraft acrylic. It consisted of a set of 3 doubled sided sanding pads and a small amount of 'polishing solution' as well as the cloth to apply it with. You had to sand the headlight in one directly with the finest pad grit that completely scratched the whole headlight (yikes!), and then do the same perpendicularly with the next finest pad. I thought I had ruin my headlights forever until I used the 'polishing solution' (which must be like a very, very fine polish) and the headlights looked like glass again. I'll look up the kit if someone wants the name as it's been over a decade now since I used it, but the headlights still look awesome. I've even got pics of it...somewhere (I just can't remember when I did it).