There is an over-the-door hanger on the back of my sewingroom door. I hang my cutting mats using men's wooden trouser hangers. Just glue a strip of rubber bubble shelf liner to the inside of the wood.
Also, we laid the sliding doors from the closet flat and covered them with flannel design wall grid. We stapled it on starting at the center of each side folding under the edge of the fabric. Then we hot-glued nylon marine rope all around the perimeter. The door shave enough space between them to leave the items up when moving the doors.