Threadless ballscrew has even less friction than the acme thread usually used for Z axis. This might not work as well. I am supprised that you experience falling. a stepper motor has some residual magnetic holding force when unpowered. that's why you feel a cogging when you manually turn the shaft. A magnetic brake that activates when power is remove is sometimes used on industrial ballscrew systems.
If you do try a threadless ballscrew, a hardened shaft will give the best results. These are available at Mcmaster.com. You will need a grinding wheel to cut it.