Magnetometer or Hall Effect sensor (for neodymium)?

I can cancel effects of gravity (calibrate) in all 3 axes,

Magnetometers are not sensitive to gravity.

The Earth's magnetic field is extremely weak, and a magnetometer designed to measure it will not function properly or maybe not at all in the vicinity of a strong magnet.

A linear Hall effect sensor might be useful. Tell us more about the project, and post a link to the data sheet or product page for your magnet.