I'd stick with Meguiars stuff, and if you go to your local autoparts shop, you'll notice they have about half a dozen different polishes. From memory, there is a diamond cut, medium cut, light cut and swirl remover. I'd try the swirl remover by hand, if that works maybe go over it with a polish, and then wax it afterwards.
Sometimes when i touch up friends cars where they have key marks under the handle, i use a bit of diamond cut, and it wont be too agressive until you keep rubbing for extended periods.