The entire width including the lip on the sides is 15".
I did just what you are talking about with thin plexiglass and double stick tape. There is room to do that, thickness-wise, because the mounting screws for the cabinet are covered with those plastic screw caps used elsewhere in the trailer, about 3/16" thick, so there is that much clearance between the door and the cabinet when closed. I used clear plexiglass pieces 14-3/4" long mounted with double stick tape, the door still closes fine.
David, Mary, and 3 Cats