Few questions, I assume you want to tap on X0. centre line with the main spindle !!!
Did G84 work before, .... can you do it with a live tool (G184) ??
If nothing works you can use a ER collet with axial compensation.
E.g. the Fahrion CET32-GB has a ± 10mm ( ½" ) compensation, you can use the spindle stop M5 and reverse with M4.
You have to drill a bit deeper than tapping because the rpm of the chuck creates a bit extra Z-value before the chuck stops.
They are available in sizes ER11 to ER40 collets.