The belly bag is an interesting idea. My only quibble is that it's something else to drag around and to malfunction at an inopportune moment. Same quibble applies to stands or other appliances.

Adding a button (or buttons) for a shoulder strap seems like a more obvious solution, assuming the guitar isn't a museum piece. Classical guitars, like other guitars, have a tail block that will support a strap button. A nice wide shoulder strap would be comfortable than hanging the guitar around your neck, is pretty foolproof, and can travel in your case.
- Phil