Removing scratches in chrome ashtray sliding cover

Third option: I've had some jukebox metal re-polished, and some re-chromed, and I always left the decision of which way to proceed up to the chrome shop. Maybe if there's a chrome shop nearby, take this to them and get their opinion, as they deal with this sort of thing all the time. If it's thin, I'd hate to see you polish through to the under (copper?) layer.