I have read about people using headlight restoration kits, but having used them on actual headlights, I would be afraid of what might happen any of the chemicals seeped inside the slab. The seal is not 100% impervious.
Maybe some rubbing compound and the buffing wheel on a rotary tool would be safer?
You might want to try wet sanding. start with 400 grit and progress to 2000 grit or better. Then a spray coat of Krylon clear. Other than that, reholdering is the only option.
Being that I have an autobody background, I'd go the route MisterT mentioned. Luckly most of your scratches are relatively in the same direction, so it can be done just be patience as you work towards the higher grits.
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