If I'm honest I tried polishing last year and using sealant and it didn't last but started to fog again due to the factory UV protection being removed.
instead i just recently went down nuclear option - took out my Porter cable polisher and used sanding discs progressing grits from 800/1200/2000 then 3000.
This left a nice haze - then I hit it with 2k Lacquer and it looks lovely - and should last for years. Cost around £10 in materials and maybe around 2 hours. For comparison I took another set to a local paintshop and whilst they took a little longer over the polishing (they took out the stone chips!) they charged me a with a discount, £75.
You would probably get pretty decent results even with a standard halfords lacquer if you take your time.
You can see the a revived headlight in my recent pepper pots thread here
Pepperpot