You can adjust the ansiotropic shader by manipulating the Tangent. Unfortunately, the Tangent node does not provide any suitable inputs - only UV or Radial X,Y,Z. However, you can generate your own tangent using the Texture Coordinates and Cross Product as shown :
Adjusting the Location coordinates of the Mapping node will adjust the anisotropic centre. To mimic the different X,Y,Z radial tangents, set the relevant Scale to zero (Z in the example image) and adjust the corresponding Location (in this case Z) to adjust the strength of the anisotropic distortion for that axis.
For info, the Cross Product returns a Vector that is perpendicular to both of the input vectors. By passing it the Normal (which pokes directly out of the surface) the resultant Vector will always be parallel to the surface. The Object coordinate then controls the angle of the tangent on the surface.
An even better solution is described here. Essentially this involves unwrapping your mesh using ‘Project from view’ from directly above the centre of anisotropy and centering the UV map at the UV origin. You then use the UV coordinates and a Cross Product with a fixed vector to generate the Tangent for the Anisotropic shader. To move the ‘centre’ you simply translate the UV coordinates.