You may want to try a chemical paint cleaner like Megs Color-X or Klasse AIO. You should also examine the paint very closley to see what is causing that gritty feeling. Is it paint defects like pitting or etching, or is it caused by a bad repaint that was never sanded, buffed, or applied correctly? You really need to identify the cause of that feel before you decide how to attack it. I wouldn't say that it is common with all cars from AZ unless the paint was neglected and not waxed. Also don't discount the possibility of a bad repaint, you should be able to tell by looking at the doorjambs, around the trunk/hood area, etc.
If you decide to go the rubbing compound route you may want to try megs #83 followed by #80, or 3M PI III RC (rubbing compound) followed by 3M PI III MG (machine glaze).