Restoring Turntable Dustcovers???

Is anyone aware of a good method of getting scratches out of turntable dustcovers? The best method I have found is with an automotive polishing compound. Any other ideas?
I've had great success using Meguiars Mirror Glaze #9 Professional Swirl Remover. You could also check your local motorcycle store for a product called Plexxus. Its for polishing and removing scratches on polycarbonate and other types of plastic windshields.
The best, and also smoothest, autuomotive polish is a professional one from 3M called "Liquid Polish-Clearcoat safe-for use by hand or machine". It comes in 1 quart bottles in either white or black. I'VE COMPARED IT DIRECTLY WITH MEGUIARS...which sucks. I've polished motorcycle helmet face shields with this 3M (besides cars, chrome, plexiglass), AND THERE IS NONE BETTER!!!
3M Liquid Polish Clearcoat works great.