I repeat. Papers do not prove ownership. Horses are sold without papers every day. There is no legal mandate that every horse's registration papers must follow that horse its entire life from birth to the end... All the papers do is identify the horse. Nothing more. That being said, at least you have THAT in your favor, and they can't claim it is a different horse. That is all those papers are good for. Vet records don't prove anything. They prove you used to have the horse treated. It does not prove he was never sold since. The lease, now THAT is gold. It defines your contract with thief #1, and proves to thief #2 that he was sold a stolen horse. You are on muddy ground legal-wise and I would get an attorney involved pronto, one who specializes in contracts, and even better one who specializes in horse matters.
You could try equinelegalsolutions.com for starters.