(Putting work hat on...)
What you are suggesting is called flame polishing.
It is a technique often used most often in plastics... on acrylic to de-burr the edges of a saw cut piece.
Basically you take a torch and hold it 4-6 inches away from the piece and wait until the finish changes, then "push" the shiny slick surface around. On professional rigs they use a hydrogen torch setup with tips every 6 inches or so... sort of like an industrial sized shrink wrap heater with a conveyor belt under it.
I haven't tried it on Lexan, but the I'll bring my torch the next time I'm down at the boat.
What it doesn't work on... anything with vinyl in it. The vinyl will go gray with not a whole lot of heat.
As far as other methods go... nothing stopping you from wet sanding the surface and following up with plastic polish. It won't be optical quality, but if a window that warps light is good enough, it'd work. Until you get to 2000 or 2500 grit it'll still looked scuffed. Once to that point an electric buffer would be nice, never stop moving it.
I don't have any experience with it, but polycarbonate is vapor polished for eye glasses, ground and polished chemistry that attacks the surface.
On my boat I'm planning to ditch the beautiful bronze deadlights and use as thick of lexan as deemed necessary backed up with an aluminum backing plate. Shooting for strong enough that it adds stiffness to the cabintop. Took keep it clear I'm thinking a piece of 1/4 inch plexi on the outside as a sacrificial layer. Lexan = bedded in, plexi just bolted up.
