Du,
The registration would work more reliably if you would crop the FOV rather than only setting the undesired parts to 0, and also set the origin to roughly the center of the cropped volume (i.e. inside the brain, in roughly the center of the brain). mri_reface has code to detect when the image origin is outside the image or near the edge (I did not confirm whether your image is close enough to the edge to activate this threshold), and it attempts to correct this by setting the origin to the center of the image volume. For your attached .nii, that code would relocate the origin from the current position near the top of the skull to the near the bottom of the neck, neither of which is desirable. Cropping and re-setting the origin would help. Setting the rest to zero, as you did, can help with the cost function once the registration gets going, but it doesn't help with the issue of bad initialization, and rotating around a poor choice of axis, due to coordinate origins that don't line up.

There are not two de-identification masks, but two affine registrations between the input and the template. These masks only influence the weighting of different regions in the affine registration cost function. One emphasizes the face specifically, and one emphasizes the whole tissue volume. Once an affine registration matrix is chosen, the remaining steps are unaffected by which was used to arrive there. 

Best,
Chris Schwarz