I prefer to use the term cosmology instead of universe. to me there is but one universe with a finite number of dimensions and an unlimtited amount of realities.

For Dr. Sarah Chambers look at the series Crusade.

Those three seaQuest doctors are actually by season. Westphalen is season 1, Smith season 2, Perry season 3.

If I had to choose one, I would go with Dr. John Carter. He has the most episodes. You could group them together and say ER doctors or something.