If scratch seems to be deep you can not avoid to go to the long and tedious process of sanding the area ;
1/ Start sanding wet with small piece of 220 grit and alittle block of rubber to be sure to sand "flat " , then clean
2/ wet sand with 320 and 400 (and liquid soap to help) then clean
3/ wet sand with 600 then 800 and 1000 then clean ( try to enlarge slightly the area )
4/ again wet sand with 1200 and 2000 then clean
5/ use polish compound (paste) medium grit and sand hardly with piece of clothe material and then polish until bright ( normally it start to be ok)
6/ use finepaste polishing ( the one to clean front car headlights) and polish to bright using a very small poliching electric tool ( you can find cheap ones at Lidl) for 25 euros) try to do a large area so the bright on the window would be "sprayed" on the whole surface
If every step is correctly done you can recover the primitive aspect of your polycarbonate...... after a hard mid day work !!!!!!
We did use this process lot of time on polycarbonate race car windshields , clear polycarbonate cockpits on planes and gliders with big success
Hope this helps
and good luck
