LazyJD, glad you also start with the involvement of your vet. Most often finding out a cuase is more of finding out is NOT the cause. For a large part of the horse owners, the cost of some of the testing can prohibit some of the tests. We started out with all the easy tests, blood work to show if there is some chronic inflammation, scope to insure all is well with their ability to breath and swallow. Allergy testing, if it tends to worsen at certain times each year, that is a good place to check. Some of the X-rays and MRI's get not only expensive but also there is a risk when you need to lay one down where the largest x-ray machine is located. It was a good idea to check for spinal, CNS involvement. We did the head films and got a good look at the atlas and axis.
The use of the thicker hair nets have always worked the best. If only a little improvement is seen. I have gotten good results using the hair nets, you need to use a full cheek bit. If the horse has a dark muzzle, the nets can almost be invisible. It is a cheap, safe thing to try in any event. The hunter that improved after moving from the east coast to rural OK is allergic to cedar, we now only need to use the nets when we show at a show that uses a lot of cedar to fill in jumps.
For a head tosser LazyJD gave good advice. Work toward straight, from leg to hand, with a good impulsion. Keep their bodies and minds busy working for you. The head tossing, and rubber neck will improve with a straight, forward, balanced horse. Some breeds tend to have a little bigger ego's, and feel quite proud of themselves.
Good Luck with your horse.