The BR-parkway is not just a road.. It is a challenge that the normal rider must take caution on.
I don't care who you are or how well you THINK you know how to ride.. The Dragons tail is one of the most challenging roads a rider will ever ride...and make it through, (if he does it right).
As mentioned above, I too would strongly suggest you ride it during the week to avoid those avid local riders who have rode it many times.
If you think your GOOD at riding, I again strongly suggest you take the ride north for the 11 miles. Stop, relax and take in the DAM view at the north end. Then, when you think you have your scruples head back that 11 miles and if you get that urge, speed up a little because NOW you know how sharp the curves really are...but don't get over bearing for if you do, you will take that trophy home of having parts of your bike on the tree of shame........
I have rode the tail of the dragon 14 times now...I choose to never ride it again...It is very hard on your bike if you ride it aggressively.
Those new tires and brakes will show the wear if you choose to do so.