I have no intention of hanging my cross bow but it seems to me it shouldn't be hard so make a rig from a ratchet strap by placing a hook, with a curve bent in the same direction on both ends, probably made from flat under the strap. The top curve would go under the ratchet strap and hold it to the tree, if you can picture that and the bottom would hold the crossbow. The curve would face away from the tree. That would be perfectly legal on public land or private land.
When you are up to your butt in alligators, it is hard to remember your intent was to drain the swamp. Stay focused!