I recommend to skip the dish soap, as any claying or polishing you do will remove any wax. Try the cleaner wax -- one with mechanical polishes like our Carnauba Cleaner Wax or others out there. Work on a small area first, working it lightly for 15-30 seconds in circular motions and check progress. There are mild polishes and repeated light actions can remove a surprising amount of "stuff." If that does not work, sometimes a distilled white vinegar and water (50/50) wash can help dissolve and neutralize mineral deposits, if that's what they are. Wipe dry and clay immediately. Then try the cleaner wax again. If that does not work, you might need a scratch remove or polish or polishing compound safe for clearcoats. Again, working lightly and inspecting your progress to just remove the deposits and any light etching. Sometimes you have etching you can't remove without compromising the clearcoat, so work slowly and inspect your progress. If you can post some photos, that might be helpful, and state exactly what you've tried thus far.