Actually there are 2 Mountains to the Sea routes. One is a trail and like the Appalachian Trail is hikers only. The other is NC Bicycle Route 2, which runs from Murphy to Manteo and follows public roads. The group ride is held twice (?) a year and only covers part of the entire route and is fully supported for a fee. I think I solved my problem with AirBnB. Out of 8 days, I've now only got 3 centuries. Unfortunately they are all in the Mountains.

Thanks for the interest and help.