For Over Under I've seen a belt "J" hook, 1-2 inch flat aluminum, leather covered. Think I can find it now, NO. I'm thinking for moving you would likely want to secure both at the break and the barrel.
You may also try and look at various SASS gun carts. Some have seats. Mine is just an open box sized for the stock and an "U" for the barrel. "U" is fur lined, Beaver scrap, and barrel is held in place by a leather strap slotted for screws. Use fur to stop barrel polishing. Fuzzy velcro does not work. Shop Goodwill for a women's fur collar. Leather strap can be found at and farm store that sells horse tack. Punch a hole in the leather and slice where it fits the screw snug.