I agree that you should NOT use a tie down.
Your horse needs training and seasoning. Not an artificial device to force him to keep his head in place.
First, at home, you need to teach him to give to the bit and drop his head. When he gets good and solid at home, then you have a tool to implement at the show when he gets "spazzy". Do not let him get away with it. Not even once.
Also, when he loses focus and is not paying attention to you, MAKE HIM listen. Do circles, backing up, sidepasses, leg yields, etc Just anything to get his feet moving get his focus back on you.
And the other thing - are YOU as the rider getting tense and nervous at shows? What you do can be felt by your horse. If you are tense and nervous and "spazzy" so will the horse. Keep your body relaxed.
∞•*˚ Βгįťţαňγ ˚*•∞
It is not enough to know how to ride; one must know how to fall.