Hi
I have a friend that has a high headed arab. I think that you should try to do so calm work, such as flat, circles, sidepass, transitions and rein back. Then try to walk around the barrels and then trot. Only do that for a while. Only when she can trot around the barrels try to do gallop trot to walk tranistions without barrels.
If this doesn't work, try a running martingale. The are unlike tie downs because they give quite a bit of freedom. You can even get ones with elastic. They only do anything if the horse puts it's head beond the point of cantrol.