"I saw some lexan film and an adhesive caulk that should do it."
All you need is something waterproof, like a sheet of plastic, a thick garbage bag as example. Cut the plastic to shape and use some spray glue to adhere it. Don't need to glue the film to the entire door area, just the perimeter. Trust me, the door panel will be coming off more then you'd think down the road, so what ever one uses to attach the water barrier shouldn't be difficult to remove and replace.
A one foot square of sound reading material (Dynamat) on the inside center of the door skin (not the area where the plastic is glued) is enough to quiet the door and provide more of a thunk sound. Some prefer to Dynamat more of the door. I'm not sure it's worth it. I've been wrong before, but only once I think, lol.