If someone makes it impossible for a third party to fulfill their agreement with me, do I have a viable cause of action for tortious interference with contract under New York law?

As noted in "No Tortious Interference Without Breach of Contract, Says NY Court" and "Why Mere 'Interference' Isn't Enough for Tortious Interference in New York," absent an actual breach of your contract, you will not have a viable tortious interference with contract claim in New York.