LOL. Marcel hangs upside down all the time. Well, in his cage he doesn't hang off his perch, but he hangs upside down holding onto the bars of his cage over his water dish and does a "nose dive" into his water to bath himself. He does this almost everyday....so funny to watch.
Also, Marcel likes to hang upside down from my finger. He looks so cute and he enjoys it.
Try this with Rio.....Let her perch on your index finger then grasp her two feet snuggly with your thumb. Start to rotate her while perched this way and she should hang upside down.
Marcel gets a big kick out of this.