OK, I know this might sound weird, but I have used Brasso to clean scratches and scuffs off perspex/plexi windows.
Apply the Brasso in sections using just your index finger. Create a wet slurry and rub in the direction of the scratches until it begins to dry. Then add some more brasso and apply with the finger again. After doing a section, gently wash off the Brasso with a damp sponge...do this a number of times. The area looks foggy but can now be buffed clean with a microfibre cloth (the kind used for eyeglasses, etc.). If a scuff or scratch persists, work on that area again.
I have been successful with everything from eyeglasses to the cover on my B&O stereo. But be careful and use this at your own risk!