This information is not quite correct. The Tail of the Dragon is on Route 129. But it is 318 curves in 11 miles. It is nice to say that you did it, but not as good as many roads in the area.
Also, if you are taking the BRP to the end (in Cherokee), then this would be out of the way. It would be better to take other roads south from Cherokee. One that comes to mine would be 441 south, to Franklin and then 28 south. That is a beautiful road, and you will pass some nice waterfalls. There are many more, but it all depends on how much time you have.
If you insist on doing the Dragon, I highly insist that you do the Cherohala Skyway. They go together like peanut butter and jelly.