Thinking outside the box.
Could you repurpose your sock to function as the example? You would collapse sail drawing it down with a line attached to the middle of the sail.
Your sock pvc hoop would serve as the opening.
When collapsed the tack, clew, and head of the asymmetrical would be exposed at the opening.
You'd want to shorten the sock. The retrieval line attaches at the mid point of the sail (the "belly button") All three corners meet at the opening so overall length will figure about 1/2 of luff(on an asym). and because the sail will be essentially doubled, the sock may not be wide enough to accommodate the thicker package. However, I can see using the plastic/resin funnel guide with a redesigned body. You could suspend it horizontally from the pulpit. The body needs a more robust material than a typical sock's lightweight nylon material. The sock requires lightweight and low bulk because it sits up near the masthead when the sail is in use. A deck location will be much more severe... water, non skid abrasion, foot traffic etc. Notice the picture you posted... a pretty heavy mesh bag that won't trap water, but protect the sail. That's why you'll see launcher pointing upward, with drainage being part of the container.
Final comment. I have researched, but never built such a system. I just decided to use the same system as my symmetrical spinnaker... which is launched out of a standard "turtle" bag. Clips to the life line, a metal hoop sewn into the top keep the bag open. Google "spinnaker launch back" for an assortment of commercially made units. I don't go to the bow, I clip it just ahead of the forward shroud on the side I want to launch from. Once it's set, I can go back to the cockpit and hoist from there... Before installing a dodger I could also manage it from the companionway hoisting and dousing from under the boom. I have found that a launch bag and a take down line work well for me...if I had a 30+ footer the sock would certainly help one person manage that much larger sail.
