wet sand the plastics with 800 and work your way up to 1500. Then hit em with some dupont acrylic clear in a can(you can get this from an auto body supply store). I have done this with spectacular results. Make sure u put the clear on thick and in 1 coat or you will have to buff em out later. I used acrylic and it worked great. Very durable, but you might find a different type of clear that might work better with plastic.
Same as above. The sanding leaves behind a dull finish, though. You have to polish it to restore the gloss. There are a bunch of plastic specific polishes as well, I'm sure they work well but I had the paint polish on hand.
I tried polishing them after wet sanding and it absolutely does not work. What kind of polish are you using? I even tried using a buffer with several different compounds. They make a product called plastic restore that u can wipe on after wet sanding but I hear it wears off after a few washes.