Whether Tandoku Undo teaches good use of the handblade, well... if you're gonna teach sword movements, get a sword. I think you'd do better to spend the time on kesagiri suburi practice. You'd learn more about moving from center, and moving the center, and moving, and proper hanmi, and extension, and ki extension, and keeping the shoulders loose, and not muscling the movement, and not allowing the movement to take you off center, and a bunch of other stuff, than all the tandoku undo in the world.
What about kesagiri suburi do you think makes it better for those things you described? Is it having the weight of bokken to play with the momentum?
Cutting across center-line with extension and contaction toward the hips? Something else?
What about tandoku undo makes it less optimal in your opinion?