Gracie, I have seen composite roofs over lanai/screenrooms in The Villages. A beautiful one has recently been done in the Mission Hills area off of a newer courtyard villa. I inspected it and was very impressed.....it gave me the inspiration to do mine. Gracie, you know I'm too nice of a guy to ever post something that someone could not do...
The company that did it was Bryan Terry Vinyl. They did a great job, complete with electrical, flat screen outdoor TV, etc. They did the roof just like mine, a composite roof with glued on asphalt shingles.
As to DEWRDW's question, I do not know of any vinyl roof made. If you are referring to a composite roof, they are made of aluminum on the outside with foam in the middle. They come in thicknesses from 3' to over 5". Many aluminum birdcage contractors do them. I'm told Bryan Terry Vinyl is one of the best. T&D, Lake Square Aluminum, etc are a few others.
Enjoy! Frank