Personally I love cleaner waxes.
While they don't last all that long they do work nicely when used for the right stuff. Mr. toasty can speak on the scratches I removed with that stuff....so can my dad.
From your desciription I would suggest a good wash, then a clay bar for the whole car, follow that with a polish. Then wax it.
If that doesn't get it out then either you will be looking at a lot of hand buffing or should consider having the car professionally buffed (assuming you dont have a power buffer)