[SvilleKid]

Well, the plastic tubes are close to the solution I was thinking of, and probably a lot more practical and readily available. I was thinking about the glass tubes some of my sticks come in! I'd imagine plastic tubes cheaper, easier to find! I'd think simple nylon webbed straps would work fine. Elastic would tend to try to make it close all the time.
main issue is how to get the straps to fold IN, instead of out. Maybe "pre-crease" each one between each tray with a hot iron, in a very limited area, so they would be predisposed to fold inward? Given nylon's melt factor, it probably wouldn't take much heat, and some trial and error should give you the right process quickly.