The way I restore headlights in my business is through wetsanding and polishing.
Tape off the lights, start with 600 grit, then 1000, 1500, 2000.
You want to wetsand to remove all the UV damaged polycarbonate; leaving a clean, smooth and even surface.
You'll then want to remove the sanding scratches with a heavy cut compound like Meguiar's M105
then clear it up with PlastX.
I highly recommend doing the last step by a machine like a rotary or those little 3" polishing kits that work with a drill from Autozone or Harbor Freight, unless you have plenty of time.
Some of my results.
This process, however, is not a permanent fix. IME, it'll last from 6-15 months, YMMV. You can extend this by keeping them protected from UV by keeping a coat or two of wax or sealant on them.
You can also avoid wetsanding in the future by hitting them with the PlastX as soon as you see any clouding or yellowing.
Hope this helps! PM me if you have any questions. I enjoy helping fellow enthusiasts.