I have the exact same problem. And I know mine is from being OTT. Pull/ slice on almost every shot.
I think I have only been able to draw the the ball one time, and hit it straight very rarely. I have noticed like you said that my finish with the driver is more on the outside of my body. And I am usually falling off balance at that point.
What is weird is when I actually line up for a draw and try to swing from the inside/out i actually still get a pull/fade just with a lower trajectory.
Thanks for posting, I will keep checking here for some good tips.
Let me know if you find something that helps..