The slop is called backlash. On cnc machines they go to some effort to reduce it through fancy gear and lead screw design. You could just go old school and take

The slop is called backlash. On cnc machines they go to some effort to reduce it through fancy gear and lead screw design. You could just go old school and take it out by how you operate the machine. If you only ever measure while traveling in one direction, then the slop will be taken out and won't matter.