Unfortunately, you will not be spending hardly ANY time at all in North Carolina and you aren't going through the Mecca of either Eastern Style or Lexington Style North Carolina barbecue.
The ONLY Q-joint that you will be in the neighborhood of that I highly recommend is "The Fiddlin' Pig" in Asheville, NC. This establishment is on the east side of Asheville, several miles off of I-26 after it parts from I-40 on the west side of Asheville.
The Fiddlin' Pig is located at 26 Tunnel Road, (828)251-1979.
I've rated their barbecue a 4.6 on my 1.0 (bad) to 5.0 (best) scale.
Good luck with your quest and have a safe trip!