I would use exterior grade plywood. I assume 3/4" thick for screen doors. Spray polyester gelcoat on an entire stack of finished doors to get edges that paint well like real wood. I'm building some guitars right now, and absolutely love PE gelcoat cuz its cheap, sands like a dream, coats nicely and is structurally like adding veneer.
john.blazy_dichrolam_llc
Delta Unisaw, Rabbit QX-80-1290 80W Laser, 5 x 12 ft laminating ovens, Powermax 22/44, Accuspray guns, Covington diamond lap and the usual assortment of cool toys / tools.