Starting from scratch (again) - Spindle encoder Question

You can use a single pulse.
Connect that pulse to A and Z of the counter and set the counter to "counter mode" so that it does not need a B phase.
Make sure you use the "position-interpolated" output of the encoder counter module.

Adding more slots for A will make things better. And a full quadrature counter would allow for rigid tapping (as mentioned). You can't rigid tap without all three phases working as the system can't detect spindle direction changes.

You could keep an eye out on eBay for "elevator encoder" as some of those seem to feature a very large through-hole and might direct-fit to the spindle.

Are there any gears in the head? You could potentially derive A and B using hear tooth sensors on the bull gear, if the lathe has one.