For dirty exhausts I used steel wool and cleaning vinegar as a rough pass, then mothers metal polish with a microfiber to finish. Sleel wool and polish works too, though on the tips a microfiber gave me a better finish.
+1 If you can get a mother's powerball and use a drill for final polish.
Cleaned up a unloved TRD exhaust over the summer using this method. Did it quick and dirty.
