I used to be a spray painter but also subcontracted to a company which supplied polycarb stuff. They needed me to repair any scratches on the material prior to delivery. To get it looking like new, the procedure is quite simple but will take some elbow grease.
In your case, I would start by wet hand sanding with maybe 500 grit (grit selection is a black art so don't hold me to it). Keep the part squeaky clean ie no sand or debris on the surface.
Keep a rubber squeegee handy to quickly dry your work to check your progress.
When you think you've removed all the deep scratches (and replaced them with 500 grit scratches) move up to maybe 800 grit.
Rinse and repeat.
Then maybe 1200 and up higher if you feel like it.
Then move to rubbing compounds; 2 different coarseness-es, applied wet.
Then polish. I used to use exclusively Meguiers Machine Glaze. Its awesome stuff. First polish with a soft cloth (I've never used a polishing machine on polycarb... it may work but I've never used one).
Final polish with Machine Glaze on a cotton wool pad. Takes forever but if you didn't skimp on the preceding steps, it should look like new.
I would estimate 5 hours or so to do a windshield. Maybe more, depends on what you're after.