We have never tried to stuff it into a couple of cases. My concern about the U.K. couple was I don't believe they made any attempt to stop the tubes from hitting each other. Steve's foam tube cozies protect more than the paint. They also wrap around his coupling ends which look vulnerable when disconnected.
Clothing can only do so much and can collect grease when stuffed around bits carelessly.
I'm glad I ordered the foam pieces which use velcro-type closures, but to minimize wrapping time its important to mark where they fit on the frame. To reduce transport bulk, half of them fit on my improvised neck rest. Thus, if and when I travel to a destination where i can leave them and return to them, the cases would be safer, faster and, undoubtedly, my parcels of choice. All of the above applies to my single. First, The older TerraTrike design used an unusual method of castering.