To answer the inital question on who to dive with, there are quite a few reputable operations out of Morehead City. I have dove and worked with all but Diver Down and would do so again without reservation. In no particular order they are:
Discovery Diving -- 2 crew boats, 1 6pax
Olympus -- 2 crew boats
Atlantis Charters -- 1 6pax
Diver Down -- 1 crew boat, possibly another by this summer
SeaTales -- 1 6pax
with Discovery and Olympus having the only dive shops in the area. If you haven't already booked, you'll probally find most of the 6pax boats full. The crew boats are sometimes easier to find a spot on but they too book fast in the summer. Good Luck.
*** the sub is ~23nmi from Beaufort Inlet at a 180 deg heading... resulting in about a 1.5 hr trip one way on most of the above vessels, under normal conditions.