Several years ago I painted the door on my 1989 22' footer. It too was faded and actually losing some of its printed woodgrain effect. I removed the door and layed it flat on saw horses, working one door face at a time. Clean the woodgrain with a strong cleaner and a scrub brush, then plenty of liquid sandpaper/de-greaser. Tape off unpainted parts and apply one coat of Petit Easypoxy, using a roller (made for polyurethanes), then tip it off with the best brush you can afford. I used one quart of "off-white" and wound up with a great job, nearly a perfect match to the surrounding gelcoat.
Don't skimp with the paint. One advantage of laying the door flat is that you can flow on the paint, leaving it just shy of puddling. It will flow out and level quite nicely.
Give it several days to thoroughly dry before carefully flipping to complete the other side. Rehang the door and no one will ever know it was painted.