I don't know about the hand position, but I am so happy for you having the breakthrough about bringing his head around.
There is a difference between asking the hrose to bring the head around and pulling it around, bu tit's subtle.
One thing I do on the ground after doing some round pen work and I am feeling close to my horse and he is happy to stand and just be next to me, I stand on his side by his head facing forward, then I reach my right hand around to the opposite sie of his jaw and put my finger tips on his cheek. I want him to turn his head all the way around toward his left hip (around me) and ultimately , I will do this, also ask him to disengage his hind end (I am standing right next to his barrel, so watch your feet!) and then with my finger tips, I try to "lead" him off walking. Sometimes it works, sometimes not.
But the point is that with my finger tips on his jaw, I kind of tap or lightly push on his jaw leftward (toward me) and when he moves, I stop. I actuallly have my hand OFF his skin, not touching him but I follow his motion so that my finger is really close. So, mac decides how far to move his head. When he stops, my finger is really close. If he then tries to put his head back , I tap and remind him NO. Then, I start with another push/tap with finger tips. If he goes the other way, I firm up and disallow him with my whole hand, then return to very gently suggesting he come MY way. Eventually he will give in fully and come well around, then I cradle his head close to me with my hand, ever so softly, but disallow him to go back. Then, I turn my body to the left so that while holding his head with my right hand , I suggest that he move his hip away from me . When he does (this is breaking him out) I take that motion and step him out forward, kind of trying to lead him by his jaw. I have limited success with the leading part. But it's fun to do .