I don't have direct experience with what you are dealing with, but you might try automotive polishing compound, not rubbing compound. Maguire's Plastx would probably work well, but doubt if you can find it in Bimini.
Put a pretty heavy load of compound on a cloth or pad and just rub and rub until the compound is gone. Putting the compound on, letting it dry, and then buffing it off does little to nothing.