To expand on this:
You want to do torque transfer; you want to have kites circling in the air turn a wheel on the ground. Your tethers can’t be too long and your wheel can’t resist the circling kites too much or the kites get too much ahead of the wheel. To allow you to use longer tethers you want to add additional wheels that you space along the tether. They need to be light and strong.
Best would be a bicycle wheel-like construction that has a central hub that gives lateral stiffness to the wheel with the tensioned spokes going to the rim, the wider the hub the greater the lateral stiffness. The spokes distribute the single-point load from the road (now tethers) along the entire rim.
If you don’t want to use a central hub, maybe because the attachment to the tethers already might give some lateral stiffness, among other things, you can mimic some of the load distribution of the spokes in your compression ring by using bridling, or by making a taller rim.
In the likely case that the possible increase in lateral stiffness from the tether attachments points isn’t enough, another way to increase that would be to make the rim wider. To still be able to stack the rings and decrease the height of the stacked rings, you would angle the rim.
…Or a different idea: let’s say you use as many rods as tethers, and you want to increase the compression they can take before buckling without making them too thick on the ground station, and generally reducing their weight. You could replace the individual rods with 3 or more thinner rods. You pre-bend them in the direction you want them to under compression - outward - and connect them together at the ends, and by spiraling a tether around them through rings attached to the rods. Now when you compress them and they bend outward, the tether gets taut and prevents any further bending. Because you used a single tether the tension in the tether is equalized. Now the limit becomes how much compression can the shorter sections/spans between the tether attachment points take before buckling.
You would make this construction stronger by increasing the angle the spiraling tether makes with the rods, making it more effective at resisting the bending rods, in the same way that guy cables are more effective then, and by reducing the length between spiraling attachment points, reducing the length of individual rod sections/spans.
You do that by allowing the rods to bend more under compression and by increasing the number of times the tether spirals around the rods. You’re probably looking for an ideal shape of the egg this new column makes under compression, so a ratio of the minor to the major axis, or something more elaborate that adds hinges to the rods.
A failure mode is probably that the rods bend outward, but come together somehow, so you end up with an arch instead of an egg. This is likely because the tether is under the highest tension when the rods make the egg shape and the rods are free to slide from this highest stored energy state to the lowest one, the arch, like a ball rolling down the top of a hill. This makes my original idea of only fixing the tether at the ends of the rods and allowing it to slide through the rings wrong. I liked that because of its less finicky construction. Now you have to compress the column and tension the tether segments like the spokes of a bicycle wheel while it is compressed. You can mitigate the difficulty of that somewhat by adding some elasticity somewhere, or by increasing the safety factor.
Maybe this is something like a Space frame - Wikipedia using different materials. I’d be interested in finding examples of this principle, but I can’t find something at the moment, except maybe this: Veritasium - World’s Highest Jumping Robot, but it’s not really. It’s probably a variant of Stressed skin - Wikipedia.
There is also this: Ali Clarkson - We Made Our Own Rope Spokes! And here someone saw that video and reached out to demonstrate the FEA software they developed to analyze and optimize structures like that: We Used Computers To Really See How Good Rope Spokes Are!