Don,
You might try using a product called Clay Magic,(this takes off all minor contaminates ) after you give it a good cold bath, then use the meguiers 3 step car care product they have, its suppose to work pretty good.

I have gotten badly stained water spots out of these 50K cads by way of using 2000 grit lightly with water and buffing with 3M's 3 step process and had real good success with it.

One other trick you can try is getting some baby powder and mixing in some water to make a paste with it and use it for a very mild polishing compound and this works nice also , you can use just your hand and a clean rag.
Then try going over it with just a tad of the dry baby powder on a rag to polish it up.............Dont laugh it works , as I did this on a 75 corvette black Ureathane custom paint job years ago and had no swirls to chase out of the paint, this was before all these High Tech polishes we have today.

SprayTech