The Z-axis has the same type of split nut to adjust for backlash. You also have to adjust the side 'clamps' on it after several hours of initial use. Getting to the Z-axis nut is not very hard, unscrew the two bolts that hold the bearing block to the Z-column and slide it up. the 'clamps' I'm talking about are the "l" shaped pieces on each side of the Z-axis truck. After several hours of initial use you notice the z-axis is a little sloppy, loosen two screws on one of these clamps, squeeze it as hard as you can with your hand to squeeze the Z-ways between the Z-axis truck and clamp and tighten the screws, do the same for the other side.
Cutting a slot is not a very accurate way to determine tool size, no matter what the tool will wander a bit do to run-out, banging on already cut chips etc.