If I understand what you're suggesting, it is that they generate a list of slight variations to the new password, has it, then compare it to the old password, r

If I understand what you're suggesting, it is that they generate a list of slight variations to the new password, has it, then compare it to the old password, right? I think many people are misunderstanding what you're saying i.e., they think you're saying that similarities between hashes correspond to similarities between passwords.