Skyline Drive / Blue Ridge Parkway
Your post is timely. We just finished a drive from Asheville up the Blue Ridge Parkway and the Skyline Drive to Front Royal, VA. We also have a 2250 Sunseeker (2015) and the trip went great. There are some tunnels along the BRP and one on the Skyline Drive, but all are suitable for your 11' height. The lowest tunnel I remember was on the Skyline Drive and was listed at 12' 8" at the lowest point, but higher in the center. The parkways are all in good shape with the exception of a 15 mile area around Roanoke, VA that is closed due to some road collapses. You will have to exit the Parkway in that area and take a detour through Roanoke. Otherwise, you should have no problems with the roadway. It is an epic drive with beautiful vistas, an abundance of short day hikes and good campgrounds along the way. We found that there was very little traffic except on the north end of the Skyline Drive which was a little busier, but not bad at all.