@rkaronde even just moving your z motors in and the idlers put will increase the number of teeth in contact for the motor pulley.
On the anti backlash nuts, there's probably no real need for them on the z axis. Unless you're planning on accelerating your bed at over 10000mm/s^2 downwards, gravity will always win and there won't be any backlash! Over time though the extra friction from using the backlash nuts might cause some wear.