But I attacked it aggressively, beginning with gentle wet-sanding on the front side with several grades of paper, beginning with 800-grit and progressing to 5000-grit. The backside was sanded with only 5000-grit. Then a low-speed orbital buffing with three grades of compound. After about an hour's worth of labor I was able to save this factory original piece, which is the goal of both the owner and myself (lower photo).
(click on an image to enlarge)