I don't use RhinoCAM, so can't really help there.
You may find it's easier to modify the M6Start macro to move to your safe Z height. Mach3 can be configured to stop and wait for Cycle Start in General Config, Toolchange section.
Generally, if you don't have an ATC, or fixed length tooling, you need to re-zero the Z axis. If you have fixed length tooling, and the values entered in the tooltable, then you should use tool length offsets, G43.
Your code should specify coordinates in either machine coordinates (with G53), or in the current offset. It's up to you how you want to do it.