A few years ago I had a deep scratch on my screen on a F650.
I have access some polishing equipment (for Glass and Fibre optics) so polished it out.
I learned not to go too hard on the perspex when polishing and use tonnes of water. The perspex will overheat very easily and get "fluffy" as if you ran light sandpaper over it.
After this learning I tried it on some small scratches on my visor and it worked quite well. If they're deep scratches on the visor it'll still work but you'll get some distorsion where you've polished.
Basically all you need is a soft polishing wheel (cotton or wool) and a polishing compound (I used Cerium Oxide) and Sh*t loads of water. Keep it really wet. Any size wheel will do the job and you can get small 3/4" cylinder shaped ones very cheap (2 quid) to use in your drill. But the bigger it is, the less distorsion you'll get.
The other option is to go to a Glass/Morror provider. I've used an old one in Dublin (so auld, I tink they invented Glass) where they have a 20" diameter, 5' Wide Cotton wheel soaked is comound and water for polishing. Took about 30 seconds and becuase of the width and diameter it won't cause much distorsion. I'd just ask them to take it easy as it'll overheat.
If you can find a place like this at a quiet time, they proably won't bother charging you...
I'd like to be in the position where I could throw away 50Euro (30quid) to replace each visor I got a scratch in...
