When I'd rig a tripod strap, I would usually put one end of the strap on a little sling about the head and one at the bottom of one of the legs: to carry, you'd have the strap go between the legs and sling that way, (usually head-down) ....this would keep the legs from any risk of unfolding when you aren't looking and snagging on something.
Bicycle tape, by the way, is also nice for covering tripods, and some will even take the foam kind of bicycle handlebar pads, which are much cheaper than those made for tripods.
And to go in a tube, to have an eyebolt, you can just find a rubber bushing such as goes on car suspensions, one that will fit inside the column's tube. and sandwich this between a couple of the kinds of nuts that have big washer-like flanges built in: put these on an eye-bolt of the appropriate size. If you put it in the tube and tighten the nut that you can still see, the rubber bushing will moosh out and hold nice and tight.
I forgot to mention, this scheme is an imitation of something you can *buy*, or part of something you can buy. At this hour, I can't seem to recall just what that is, though. (aha. I'm thinking of a boat part or something. I don't know if they come in the right kind of size as a piece. But you can get the parts.)