I responded to another post with this information, but then realized it needs to be its own thread.
Micro Mesh sells paper up to 12,000 grit. That’s right, 12 Thousand!
Their products are intended to refinish airplane windows, among other things.
If you contact them, they will send you a free sample kit containing all grits they make. Otherwise, it is about $15 for a kit (Rockler and Woodcraft have them)
For deep scratches, start with the 12,000. If it doesn’t work, work your way back through the grits (8000, 6000) until you notice an effect. You will have to refinish the entire screen.
Once done with the MicroMesh, use plastic polish (Novus is one brand) for the final step.
The Novus might work by itself for very fine scratches. Try it first before using the Micro Mesh.
Make sure to Read ALL instructions!