Try Meguiars #17 Plastic Cleaner, it will remove deep scratches[not gouges] from plastic windshields, motorcycle helmets, CD's and most anything made of plastic. My used helmet looked terrible, it now looks new.
At Autozone for sure, some mom & pop auto "body shop supply" shops will have it also.
It's $5.95 and also is good for your plastic headlight covers that all modern cars are equipped with ..
Doc
BTW, polish from inside to outside ,, NOT round and round..
edit;
found linky
http://www.meguiars.com/product_show...cfm?SrcLine=PI
This is the online p/n for #17
M-1708 ....................8 oz. $6.25
I suggest skipping step #2 which is #10
M-1008 ....................8 oz. $6.25
Step 2 is for only final polishing of eyeglasses etc, I find the #17 makes a mirror finish to anything else.