A paint cleaner may work better than simply a polish. Paint cleaner will chemically fix it, polish iis abrassive and more for scratches/swirls.

Meguiars has one ,Mother's has one...ect. There's also Meguiars ColorX which is a sort of cleaner/wax that stresses the cleaner. If I had something that I knew had good cleaning I'd send some to you but really--I don't at the moment