OK, here are a few thoughts:
Make a paste of baking soda with a smidge of water. Use a cloth (or a toothbrush / denture brush) to rub that around. Finger pressure may be required. Non-toxic, helps deodorize the reefer too.
Toothpaste - apply and use same as above.
Two products from NOVUS. #2 FINE SCRATCH REMOVER. This is a very fine rubbing compound I use on my motorcycle helmet face shield if something scuffs it. Rub and rub and rub, then rinse with warm clear water. Then use the
NOVUS #1 PLASTIC CLEAN AND SHINE. Awesome stuff, works really nicely.
I find the Novus products at a motorcycle store (i.e. Cycle Gear), a motorcycle dealership or check out NOVUS Plastic Polish