Micro-Mesh makes a kit for removing scratches in plastic. It is their "KR-70 Acrylic/Plastic Restoral Kit" as used by the military for hazy windows on airplanes. The kit comprises a number of abrasive sheets in grits from 1500 to 6000, along with Micro-Gloss liquid abrasive. It is meant to "remove light damage and restore optical clarity." I have used it successfully to polish some heavy scratches out of watch crystals. It works so well that the crystals look like new.
(They also make a "Plexiglass Lens Repair Kit" with grits from 120 to 12000 and is priced around $18.)