If we imagine the torque transfer ability of a tensioned soft shaft is proportional to (tension mediated resistance to compression) \cdot(tension mediated resistance to twist), then introducing rigid elements to resist compression like Rod and others are doing, but also what I think is a relatively novel idea of introducing rigid elements to resist twist should both reduce the tension needed and increase the torque transfer ability of a shaft.
If you’re interested in being able to wrap the shaft around a drum, four ways I can see of doing that would be to either [1] make a number of chains of thin dominoes with two channels for two tethers and leave enough clearance between dominoes to be able to wrap the chains around a drum, or [2] to make fatter dominoes and leave more clearance between them and allow them to move freely along the tethers, but now after unreeling the chain, block the dominoes from going back onto the drum and reel the tethers back in slightly to tension and stiffen the shaft, the same idea as this collapsible string toy, or [3] replace the tethers with something like a leather or TPU belt, or [4] use inflatable belts.
Because the resulting belts or chains are going to be slender, they will sag if they are not hanging vertically down. If you’d like to reduce that you could make them thicker. For that methods [2] and [4] make most sense. Or you could connect the different chains together at intervals like a space frame so that you have shorter spans and the chain stays in the correct orientation better. Reeling them in and out becomes a little more challenging then I think though.
If you’d like to test the idea, you can make a chain, hang a weight from it, and see if you can make it move against a resistance, like air resistance, or can move the weight against gravity. You’d also test to failure and note the amount of torque and twist and deformation at failure, and see how you could improve performance.
Like all things, this has benefits and drawbacks. Some benefits could be a narrower shaft and less shaft tension needed. Some drawbacks could be more weight and complexity and limited scaling ability.
To compare different solutions with each other, I think you need a metric like voltage drop or efficiency per meter. You’d try to model the efficiency per length and compare your model to measurements. Inputs could be radius of the shaft, tension, untensioned resistance to twist, resistance to compression, elasticity and damping of used materials, Cd, area and distance from center of peripheral tethers, weight per meter, and so on. If you have a metric like that you could even compare it to things like conductive tethers or rope drives.