Would it be worthwhile to rig up a spring to over-counterbalance the weight of the Z components? This would pull the nut up against the "under" side of the screw thread. It might also improve Z axis performance since sometimes a little bit of binding, plus the weight could cause a stepper motor (if that is what you are using) to loose a step or two.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)