The best way to totally remove the scratches is using a micromesh kit. This stuff has the sanding materials and liquid to polish out some severe scratches (I know I have polished aircraft canopies for fecking hours) it also recovered a Mondeo headlight that was all but fooked. The only issue is that if you remove a lot of material it distorts the view (not really a prob on a screen). Like this http://www.eternaltools.com/micro-mesh-polishing-kits/
Be really careful if you use the micromesh though, start right down on the very fine first, some of the higher grits feels smooth to the touch but rip the feck out of plastic then you have to spend a week sorting out your own mistake