I like the idea of the tank tread rolling on a rack and I think it should have great stiffness. I had a crude conceptual sketch but the devil is in the details. It might need a nontrivial preload to maintain good contact between the belt-pinion and the belt-rack, but if someone can pull it off it would be great.
I am not sure how you are concluding that the twist is small. It sounds like you are comparing the belt stretch without twist (applying the force to the rollers) and the belt deflection with twist (applying the force to the tool at various Z), and allocating the difference to twist. I’m not sure that is valid because the adds additional deflection to the tool that you have to measure at the tool. One would expect the belt deflection to be the same regardless of where in Z the force is applied but the tool will not deflect the same amount.
Am I incorrectly understanding your measurement?