Yep I agree, Novus Deep scratch cleaner followed by the Fine scratch remover/polish & a couple of microfiber cloths for each stage of the cleaning. good stuff! works well on plastic lightup signs on Coke machines too.
or if you are in a hurry, many people have had success with automotive headlight cover scratch removers.
I've used the headlight scratch remover, it works pretty good. with they kit, you are basically wet sanding the film off and scratches out then polishing it to a nice clean surface. It was pretty bad and came out pretty clear. if you are starting with pretty good, I think it may work very well.