An idea ran through my mind as I read your needs of a quick access holder. Some tools are involved but it’s real simple and not expensive. A piece of pvc used in sprinkler systems, maybe known as thin wall or schedule 20. A router or table saw, maybe a Sabre saw. Cut a groove down the side of the tubing wide enough to accommodate the bigger eyes of the rod, and drill a couple of holes at the thwarts (cross members) and thread a zip tie through the holes and around the thwart. You can probably see where this is going, hope it helps.
Creativity is just intelligence fooling around