Rich, not sure what version of Z-axis you’re on - but check your set screws to the Z-motor.
This can happen on the stock belt drive Z and the HDZ (there is a different possibility on the Z-Plus). If the connection from the motor to the belt drive or the ball screw is loose, it will cause a behavior like this. Essentially the motor slips in pulley or coupler connection as it moves each direction. It can look fine and stable when not under load, like homing, zeroing, bit changes. Under load is where the unpredictability begins because the forces are more likely to cause a very slightly loose pulley (stock Z) or motor coupling (HDZ) to slip.
Note - on my HDZ the lower part of the motor coupling was not tight when I received it, good reminder to check all the bolts, v-wheels, belts, etc. even on a new piece of kit. 