PVC trim expands and contracts considerably more than any wood species. Stand alone frames will deform under direct sunlight. Screwing them in is the way to go. PVC trim should remain a light color if it's painted, sun melts the stuff if it's painted a dark color. I heard that there's a special paint you can use to get darker colors but I can't think of the name off-hand.
I'd look into having the screens pre-made with an aluminum border, and then embedding them into a PVC frame. Could be as easy as making the frames out of 5/4 stock and plowing them out with a slot cutter, and assembling around a pre-made screen.