Aloha No Heney,
I have seen simple green (diluted) and orange based cleaners recommended, spot treating and a soft brush (like a toothbrush). Rinse quickly with clean water and let it dry. Then a coat of 303 should help.
I imagine a gentle spray-on laundry degreasing product would also work, if it is friendly to nylon (Dacron).
Mildew is another problem that sometimes is associated with dirty sails, but it takes a different approach. I have yet to experience this issue in Hawaii, though green stuff is growing everywhere right now in our rainy season. It's a good idea to avoid rolling and storing the sail while it's wet.