At this point, I think a video would be the best thing. Because right now, we are simply guessing what may be happening when he starts throwing his head.
Definitely get his teeth checked out, if he is already 6 years old and has never had it done. It's very possible he could have an issue there.
It also never hurts to have a chiro check him, or a lameness specialist. My guys get an annual "wellness exam" every year, to hopefully pick up issues BEFORE they become an issue.
Now as far as working the barrel pattern. What happens if you WALK the pattern 3 times? Does he also start throwing his head?
Now, I am not one to do the pattern X number of times. I am going to work the pattern until I get accomplished what I want. If they get it perfect the first time through, wonderful! We are done. But if I've got to do it 5 times until they are focused and responding, then I will (almost never gets to that point). So don't set it in your mind that "we are going to do the pattern 3 times". Rather, base it on how your horse is working. When he does something right at whatever pace you are at, leave him be.
I'm a big fan of doing drills with the barrels .... but not actually the barrel pattern. This allows me to work on the barrels without souring them on the same pattern every time.
I went to a Judy Myllymaki clinic this spring it was awesome. If you scroll to the bottom of this page link
Myllymaki Barrel Horses
You'll find lots of her stations she uses. They are great!