Actually, if a bitcoin-like system is used to manage property rights, the problem you describe doesn't arise. There is no need to prove that Party B owns the private key used to sign the contract because the property in question "belongs" to the private key, not to Party B.
To make an analogy with bitcoin, when you transfer it, there is no need for any party to prove that you are really the owner of the private key, because it doesn't matter. Even if you later claim that someone stole your private key, you won't be able to reverse the transaction.