For what it's worth:
Many year ago when I was in the ATC (Air Training Corps,) if I was a naughty boy I was given a tin of Brasso and a rag and got told to clean the Perspex screens of helicopters.
Brasso is a very mild abrasive, but is abrasive enough to 'cut out' minor scratches in plastics without damaging the material itself.
Perhaps there is a similar brass cleaning/mild abrasive product available that would do the same job for you?
Just a thought . . .