I FINALLY got something workable. I've been trying to design a functional twist-collapse hoop for the last three weeks based on this

http://www.hooping.org/archives/cat_hoopmaking.html

Note: all of my trials were done with 160 psi, 3/4" PET irrigation pipe. For filling the gaps between the shaft of my "bolts" and the connector inner diameter, I used some flexible shower-curtain vinyl that sticks to itself. I cut that into strips the same width as the connector's length, and wrapped it around the bolt shaft. I could test the fit of the connector over the bolt until it fit just right. That way, the bolt didn't wobble around inside the connector.

Anyway...
The first hoop was done with two spinning connectors, each placed on opposite sides of the hoop. These first connectors were made using large steel bolts and nuts that mostly filled out the connector. The result: an incredibly heavy hoop that had an eccentric orbit. That is to say, on the first revolution it would hit my right hip just right, and on the second revolution, it would hit too high or too low, and on the third revolution it would go back to just right. It was hard to control this, though if I spun it harder, it would level out. If I moved at all inside the hoop, it would go eccentric again.

The second try was done with a smaller steel bolt and nut inside an aluminum sheath, and using washers on either end to keep the bolt from slipping through the connector. The spinning connectors made this way weighed a bit more than half what the full-steel shaft connectors weighed. I tried installing just one connector. The result: the hoop would spin "phasically." That is to say, the hoop would spin at the same speed on each rotation, except for the rotation where the connector went off my body. Once the connector lost contact with my body, it would spin significantly faster. So I couldn't keep time with music. I put a second connector in to oppose the first one, and ended up with the eccentric orbit again.

I may have finally discovered the best materials: Nylon all-thread and nylon nuts. I used two nuts on either end to create a lock-nut situation, which eliminated the need for glue (and then you don't have to wait for glue to dry). I figured that having the two lock-nuts on either end would maybe distribute some of the tension through the nylon all-thread shaft, but I'm no engineer, so it's wishful thinking.

I just built one of these and tested it with only one connector. It is light, and very responsive. WOOOO-OOOOT!

The downsides: 1) I don't know how well the nylon will hold up to repeated twisting and the stress of spinning; 2) The single connector causes more tension on the wide glitter tape that's on this hoop, and the tape gets little rumples in the inner diameter of the hoop that run perpendicular to the length of the tubing.

I think I'll add a second connector later to add a little more weight, and to maybe eliminate some of the tension on the hoop tubing itself. I think they collapse better with two joints than with one. But I ran out of 160 psi tubing, and the 200 psi tubing does not work as well with my connectors. And I don't want to modify this first perfect hoop. Grrr...

But still, YAY! I can't wait to test it out at the gym.

Edit: I got inspired and tried to add a 2nd connector to the hoop, and bent the hoop. :(
Managed to salvage both connectors and put them in the hoop that had the metal connectors in it. SUCCESS AGAIN! Two connectors definitely improve the collapsibility of the hoop, and performance and response is actually a little better than with just one connector (due to the extra weight).