Another technique would be to use a French Cleat.
A 45 deg angle of wood or aluminum.
You could custom fit one in the beveled area and get it flat to the wall.
You could put one on the bottom too for stability.
I would use a standard picture wire technique. Either one span for two wall anchors, or if that would show above the frame, use two shorter ones.
Purchase a frame hanging kit, which would include the screw-on eyelets, or just put screws into the frame and wire to those. You might have to experiment a bit to find out how much slack is needed in the wire.