You're gonna have to team up with somebody to get quality. I know it is done, but trying to get a decent video of the shot with a motionless camera is not going to work. Hence, your ? about the hat. Won't that be heavy? And, how do you know it is pointing in the right direction with the quarry centered?
I've been filming enough to realize that a partner is needed. You are the designated hunter one day and they are the next type of deal. Or better yet find a nonhunter.