Brian, I would stay away from using the z key for that as it is a native mach key in the default screen. If your doing a screen from ground up, it should be OK but be careful, lots of gotchas in modifying one. Mapping a key to zero the z axis dro is simple enough. First, copy your screen your wanting to modify and rename it something unique. Then open it in screen 4 and choose the button that zeros the dro and assign the key as its hot key. I think there is a screen 4 tutorial in the videos section.
Brett