The late Roger Rees would have made for an excellent Doctor, even if the tendency was to cast him as a villain.
It never happened, but I could always employ a bit o' wish-craft and make the claim that he did play the Doctor in another TV dimension.
So why not claim that Lord John Marbury in the 'West Wing' dimension was actually the Doctor? Somehow President Bartlet knew who he really was, perhaps based on Marbury's experiences in dealing with the India and Pakistan disputes. (There may have been a Vespiform involved in that as well.....)