Have you tried Automotive rubbing compound. It comes in various strengths and grits. Use gentle pressure on a small area to test. Then wax with a good auto paste.
Also LimeAway can be used to remove mineral and rust stains. Just be sure to read the instructions first to see if it is safe for the materials you use it on.
-"You want to make it two inches - or, if you're working in centimeters, make sure it's enough centimeters for two inches."-Red Green