I am pretty sure it is trivial to change the orientation of a VOR. Although the antennae are fixed, it is the relationship between the phase of the 'rotating' signal versus the omni reference signal that gives the radial. Changing the phase of the signal is undoubtedly trivial.
At the risk of thread drift, anyone ever used or seen used a transponder ILS approach ? This works on exactly the same principle, to generate a pseudo ILS, valid only for one aircraft. Are there any in actual daily use?