Go to Lowe's and get a roll of 2" foam insulation that is designed for window air conditioners, etc. It should have a two sided tape on it. Put that on the back of the dibond around the outer edge. A double cleat system for the top and bottom will hold it in place well. A piece of one by four cut in half with the blade on a 45 will make your cleats. One 8 footer on top and bottom. Screw the cleats to the board before lettering. put in place then screw from top and bottom to join the cleats. Just my two cents and I am sure there are a million ways to do it.