One idea would be a long, narrow silnylon (or cuben fiber) stuff sack for tent poles, with the sack's micro-toggled drawstring located at the open end of the tube, so the tube w/rod could be stored inside the stuff sack with the tube's open end secured by the toggle.
Fibraflex has a silnylon tent pole stuff sack which, at 31" long, might contain the tube you have. It's called "MOONBOW Sil Nylon Pole Bag (31") with Box Bottom & Tie, 0.4 oz" and costs $6.00. See link below, at the last item of the first category ("Part") --
The open end of the Fibraflex stuff sack appears to rely on tie-offs at the open end to keep it closed, rather than a drawstring w/toggle. Tie-offs might work, but surely not as securely as toggles.
Another drawback to the Fibraflex stuff sack is that it is probably much wider than needed for the tube you describe.
Guess you could get a plastic tube w/larger diameter to fit the sack, & carry more rods.
Or maybe a MYOG project, if you think the concept would work for you.
There's another option, too: ask Zpacks to make a cuben fiber stuff sack with toggled drawstring, custom fit for the length and diameter of your tube. See the following link at about the middle of the page for ZPacks' "stock" tent pole stuff sacks -- stock sizes are too short, but gives some idea of possible cost and weight.
TrailLite Designs sells (and makes?) a Tenkara rod carry sack called "Ebira Rod Quiver" -- which simply a long narrow sleeve made of Dyneema X, with a toggle/draw string closure at one end, plus extra features like daisy-chains on the side for attaching a zipper pouch to store line, flies, etc.
They also have a cuben fiber version of the quiver (UL Ebira).
See descriptions and photos at this link, mostly toward to bottom half of page:
Haven't seen any of those "Ebira Quivers" that are long enough for a 30" tube, but the quiver illustrates what might work to secure a rod in a tube.