Machining Polycorbaonate Sheet

I have completely removed machining marks and got a clear finish by hand lapping the surface, using a surface plate and very fine polishing sheets. But this only works if the surface to be polished is flat.

As far as solvent polishing, the solvent used is Methylene Chloride (not to be confused with MEK). Absolutely do this in a well ventilated area... like with a fan blowing on you. Don't breathe the stuff, and wear gloves to keep it from your skin. Incidental contact won't instantly rot your skin, but it should be avoided. After getting the surface as smooth as possible with mechanical methods, dip a corner of a lint free cloth into it and rub the surface to be polished. Continue until it's clear. Don't let it drip. Crazing may result if you try to remove marks that are heavy, but if you pre-polish as best you can and use this method as the final touch to clear up the cloudiness, you can get beautiful results. If you are worried about crazing or cracks, and you have the time... do one part, or a scrap part, and them wait about 72 hours. Any crazing that will happen, will happen in that time frame.

Practice on scrap until you get the technique right.

Vapor polishing is the best way to do what you're trying to achieve, and there are ways to DIY, but I wouldn't attempt it. If it's worth it to you, OP... find a local vapor polisher, or have it sent out. Your part will come back crystal clear. It's basically same as solvent polish, but the solvent is heated inside a small chamber and the vapors do the work.