... riding like I'm on a dirt bike; keep it upright while braking into the turn, ...
This.
Mines road, Morgan Territory road and ones like it, require a a some what different approach. The more you ride the road, the better you'll be since you'll know the corners better. Single lane roads become especially challenging since you must accomodate the unexpected should you encounter another vehicle. Since that road is not heavily traveled, especially during the week days, many people don't expect to see another vehicle. On parts of the road, you can glance ahead across the side of the mountain and see a vehicle coming the other direction and therefor anticipate when you'll have stay further right. Otherwise, when entering a blind corner, if you're on the mountain side, stay on the inside but expect debris and expect a vehicle. Stay on top of the bike, like PlaneGray suggests, and when leaning in the corner, lean the bike into the corner not you. If you've never ridden in the dirt, this may seem unnatural. Also, personally if I'm in that kind of environment, I tend to run lower air pressure, YMMV.
Your Ducati is a good bike for that road, I prefer my sumo when I head up there. Something light and with a more upright seating position, makes riding that road fun once you're used to it. I've ridden bigger, heavier bikes up there, such as a few sportbikes and a Goldwing. And for me, a liter sportbike can feel like you're wrestling a bear on parts of that road.
It's a fun road, but you have to know the road, understand the traffic, and respect the conditions. I've encountered a huge bull lying in the road chewing its cudd along with all the other things mentioned by Hooli, so stay aware. :thumbup
