I would personally recommend Novus polish products.
I use Novus 2 a lot to clean plastics on all my pinball machines and even on the playfields. Most of the plastics I am cleaning are non replaceable (or at least not easily) and Novus does an excellent job. It takes dull, yellowed, dirty plastics of any kind and makes them look perfect or nearly perfect. I usually use Novus 2 to start and then finish with a wipe of Novus 1. I have never had to use Novus 3, as none of the scratches have ever been that deep. If you ask anyone that owns a pinball machine it is the only thing they use because it will not damage the piece you are working in.
Note - a lot of elbow grease is required. A buffer might be in order for such a large surface like a window.
I don't find the Novus products that hard to find but I am usually ordering pinball parts anyway. I believe the products to be readily available on Amazon. They are not cheap but they do work.