I worked through head-shyness with Willow using lots of carrots. It worked, but she really did expect carrots during the bridling process ever after. I did some research on techniques for working through this problem and found a video I really liked. I have no idea who this trainer is and can't vouch for anything else he does, but this technique works.
On Friday I spent forty minutes rubbing Dakota's neck and head. At about twenty minutes, I started brushing past his ear. By the end of the forty minutes, I could rub his ears without a fuss. Then I started working the head-lowering technique, which worked right away. Then I used an old thin leather rein as a "bit," and had no fuss there either. I quit and let all that percolate through Mr. D's little head for the night.
Saturday I started the head and neck rubbing again and could almost immediately mess with his ears. I repeated the head lowering and the leather rein "bit," and it all went so well that I got the bridle out. On it went, no muss, no fuss. Good boy! Then I lunged him off the bridle. It was much better having the extra control. No more shooting off the circle randomly.
Dakota got the day off today, but I went out in the late afternoon to give him carrots in the pasture. I don't want him to think every time he sees me I'm going to make him work. I'm delighted to see that Dakota already has a BFF. The two of them are always grazing side by side a little ways away from the main herd. I think the friend is a roan Appy; I'll find out for sure. Forgot to check if it's a gelding or mare. He/she gets carrots from me too for being a friend to the new guy.