I hung my folder exactly the same way using a D cell Maglight plastic clip holder. The 20x1.5 tires fit perfectly into the round clamp.

Also on a super narrow road bike, with folding or removable tires and a flat type handlebar, you can easily store a bike in a very thin space like behind a couch or even folding bed. Just loosen the quill bolt and rotate the handlebar parallel to the frame, fold or remove the pedals and slip into that thin space.