Sanded them down and buffed. I started with 600 grit sandpaper, wet sanding until the old oxidized coating was gone, then went up to 800, 1200, 1500 and 2000 grit wet sanding each time until all the scratches from the previous sanding were gone. Then just some plastic polishing compound and buff until they were shiny, put a coat of thinned urethane (1 part spar urethane, 1 part mineral spirits) to protect them and buffed one last time.
In total, it cost me ~$25.