Hi
Unfortunately you can't, because what you want is made by a rotary axis (usually the C axis) that can only be operated by a servomotor.
In general, lathes that have a C axis have an additional motor (Servomotor) that is engaged when needed, becoming an axis that can be synchronized with the rest of the axes.
There are also Spindles that can synchronize with the rest of the axes (C axis), but the controller is a bit more special.
Your problem is that you have a normal motor controlled by a VFD on the spindle.
Even if you want to do spindle indexing, you will need the Z channel of the encoder, because the first thing the spindle will do, will be to check the starting point given by the Z channel pulse, depending on it will make the required position.
If you could implement in mach 3 both the encoder and the hall sensor, as a Z pulse, then you could do indexing.