Rather than tryign to figure out how to get the boat name to adhere to the material currently in place, why not consider making a mounting plate. Drill and screw or bolt a 'placard' to the starboard which WILL allow the name to be adhered to the placard rather than the starboard. Think of the older wooden boats that carve the boat name into a wooden sign, then mount the sign on the transom, rather than carving or painting the transom itself.
The door is thin. You can screw a rack into the door, however I'm a big fan of through bolting things with a nylon lock nut on the backside. Vibration and pounding have a way of making things work loose over time.