I don't get how this would prevent the leakage of private keys at all. My attack does not need to know what the message is, and it does not even need to know what the private key is. It just creates a choice of k in a way that enables the attacker to extract k from two signatures. If one knows how the wallet implementation works, it would be enough for this attack to just inject the right random numbers into the wallet's entropy source.
Go look at what a blind schnorr signature looks like mathematically. Without knowing the blinding factor the signer has zero knowledge about the resulting signature... it could literally have any value, so they're unable to grind it or pick it in a trapdoored way.