My windshield gets occasionally grody, I use terry cloth towels...but the thing that I think makes the biggest difference is this cleaner called 'Dirtex', this stuff works wonders comared to a popular brand. I always find it alongside commercial supplies. One day I had a chance to compare 2 cleaners side by side, with the dirtex all I had to do was one run, and a buffing...with the other stuff I quit after 4 tries and reached for the dirtex. It will remove housepaint, so you really ought to go over your dash with a protectant to be sure that any overspray hasn't done any harm to your dash. My dash tends to need a cleaning usually around the same time as the windshield anyway, so I kill two birds with one stone. Seeing that you live in Largo makes me think that it maybe the outside of the window that is either weatherbeaten or possibly that film that you tend to get on your windshield when you live near saltwater, esp. on the east coast. Try doing the outside of windshield again, even just in a small area, and see if the refractions continue to persist.
my 2¢
-Larry