I find that the third batten down tails off to looard often when the other ones are flowing.
That said, I wish I could answer your question. Can't. There's a good article here: http://www.sailinganarchy.com/article.php?get=1134
that I have skimmed but not picked through about fat head sails.
I suspect the third batten down is the "borderline" between the lower part and the square top and that the upper part in higher wind rolls off beginning at the border. But that's just a guess.
Pretty confident that ways to keep a good sail shape in various wind conditions can be had without adding a lot of extra controls.