I am sure Woody does not need this type of treatment yet, but if it gets worse and worse, you could try a shock collar. Ceaser Malan (Discovery Channel) delt with a bad case of tire biting with a Blue Heeler. The dog would bit all sizes of tires, moving, or parked. The dog was only 1 year old but had been run over 3 times, and as a result, she already lost 1 eye. If Woody obsesses over it, and never gets better, then I would suggest the shock collar. This way you can "punish" him even when he thinks you cant see him. If he happens to do it to tires when you are in the house/barn, and he is outside. It really worked on the dog Ceaser treated. The owner jumped in the truck, and started it. The heeler started to stare at the tires and "obsess", and before he could go for the tire, Ceaser shocked him. He ran about 100 feet and layed down. It only took the dog about 2 shocks and it was totally different. I never ever even let the thought of a shock collar as treatment run through my mind. Now seeing that a professional dog trainer used it properly, I would use it if my own dog ever got really bad. It is especially good if you are always alone, and nobody else can help you scold the dog.
There is my 3 cents. Not really reccomending you use it now, but if nothing else works, you could give it a thought.