Are you confident that you're only experience inaccuracy on Z? Does this happen on air-cutting or only when cutting material?

If air-cutting:-

Write some g-code to test each axis - X, Y , Z independently, measure Z height at start of each axis. Run each axis for 10 minutes independently and re-measure Z.

I expect that rapid slews on X/Y will not impact Z height at all.

If you lose Z height on the Z-axis test only then I'd be concerned that the Z stepper is possibly stalling, or otherwise missing steps. Missing steps is perhaps unlikely if your other axis are okay and the control system is the same for all, but it could possibly be one stepper driver (Z) is more on-the-edge than others. Check Mach's stepper driver pulse widths are sensible for the stepper driver (or just change them to 5us anyway).

If this only happens when cutting material:-

Is this possibly the stepper stalling when trying to plunge into the material - check the Z stepper driver current setting.