@wesc do you actually need the backlash compensation in Z?
Typically the weight of the bed will always keep the gearbox loaded on one flank even when you reverse directions. You'd only go across the backlash if you are using z accelerations approaching 10000 mm/s^2 (I.e. 1g) where you are outrunning gravity. Granted a bit of friction might make that number smaller in practice, but I doubt you'd be anywhere near those limits if your motor has to run through a 10:1 ratio.
It's different on X/Y axes where you don't have gravity always pulling in one direction. I know I've seen many printers with 'anti backlash' nuts on the z lead screws, but they just don't make sense to me from a physics point of view!