I am not familiar with your controller. However, there may be parameters that you can set which will assign a G53 machine position to the home position. It sounds as though the control is currently just inserting zeros at those positions.
You'd have to determine the actual Z distance to your desired zero point at the chuck and insert that in the proper parameter.
Sometimes you'd have to shut down and restart a controller to make a setting like this stick.
Another less desirable method would be to command a G50 (G92 in mills) position when the turret is at home. This has the effect of shifting the G53 coordinate system and typically drags all the related work offsets along with it. The disadvantage of doing this is that setting does not stick between power down/power up sequences so you'd have to do it manually.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)