Though the 3drefit option is useful for display inside the AFNI GUI, it won't work well with most AFNI commands (including 3dcalc and 3dNLfim) that assume the same grid (coordinate system) for a dataset and a mask. 3dcalc will issue a warning but will compute on the corresponding voxel based on index not true x,y,z. You can still get around this with 3dresample, but that obviates the need for 3drefit in the first place.

The Nearest Neighbor recommendation is the way to go here with 3drotate. You can use the Nudge plug-in to move the mask too, and you can also save the "nudged" dataset. Various interpolation methods, including nearest neighbor, are available. Use the "Print" menu there to print the 3drotate command to use in a script or command line.