Never tried it on perspex but toothpaste (not the gel but the old style paste) works really well on scratches on glass, you could give that a try?

i think you can by a product from harley store there is 3 products  one is could wind screen perspex cleaner    one is fine scratch remover  one is deep scratch remover    hope that helps cheers

Novus is meant to be good:

www.novusaust.net.au/novus-auto-glass/plastic-polish.html

I would suggest that you give these guys a ring first and see what they say - Handcraft Fibreglass, 19 Prince William Drive, Seven Hills, Ph: 02 9674 3586.

I have used then several times to make and trim screens and found them to be very helpful.
 

Chopaweeza

Have a look at this Meguiars product called "PlastX".  It comes in a 298 mL pastic bottle.  Here's a link to Meguiars web sit.

http://nedswear.com.au/

You can get it from Super Cheap Auto for either $18 or $19.

I use it all the time for the screen on my 03 Ultra.  It will not remove big deep scratches but it will remove smaller blemishes.

Hope this helps.

Cheers Kymbo