You could build a frame with a rabbet deep enough to accept a 1/2" foamboard back, OR a 1/4" pc. of Luan underlayment grade plywood. You could glue the frame to the backing. Foamboard and plywood do not expand/contract much so the frame should stay tight.
Your picture frame could be assembled directly on the wall. Use a wide material for the frame with a 1/4" rabbet around the inside. Mount the bottom first, dead level. Mount one end, perfectly vertical. Set the map in the frame. Mount the other end then the top.
Large museum canvases are sretched across a frame of wood with a non acidic cardboard or other medium that will not harm the piece. Maybe you could build such a frame.
Tom in KY, a glass cover would be best for it's hard, easy to clean, scratch resistant surface.