First of all, you have misunderstood the BXSF file format. It's not four 4x4 matrices, and also the data contained in this file doesn't map over to any xyz format, nor does it represent the Fermi surface. It contains the eigenvalues of the bands, and the Fermi surface is rendered as an isosurface interpolated to energy=0.
ATK has its own module for computing and visualizing the Fermi surface, but at the moment it doesn't have the capability to compute the volume of the Fermi "blob", but this could be a nice feature for the future, we will keep it in mind.