hi mate, from my limited use of mach 3 I've overcome this problem in the following manner.
Pause program (take note of current Z axis value), set manual jog speed to low %, jog up/down to required depth, click on the Z value readout box and re enter the previously noted Z value and continue program....that way the tweak is done by adjusting your zero on the Z and not in the program.
You don't always have to jog, if you know how much travel you want to add/remove just type over the axis values and hit enter

Hope this helps.
Dan