There is a tunnel several miles in from the north entrance to Skyline Drive on the Blue Ridge. The ranger at the gate didn't mention it. It is marked 13 feet, and my rig runs 13'3" to the top of the forward AC. Fortunately, the tunnel has a Roman arched roof, and I was able to go down the middle. Also fortunate was the fact that I didn't encounter any oncoming traffic.
The alternative to going through was backing at least four miles as there are no turnouts long enough or wide enough to turn a long fifth wheel.