Paul a DIY workaround is use some white toothpaste for rubbing the windshield. Clean your windshield with plain water, apply some toothpaste on a piece of baniyan cloth & rub it. After few rubs you can feel that the rubbing movements is getting smoother which shows that the toothpaste is removing contaminants . Preferably start doing it from the passenger side so that you can really see & feel how well this technique works. This is a proven technique & you need not worry. The theory is quiet symbol. Tooth paste has this micro particles which act as an abrasive compound which rubbed against the windshield will remove the contaminants. Yes this is the same happening with your teeth too .