First of all, thank you for your insightful speech. And it is really happy to see you again.
If I remember correctly, you think that sophists are not purifiers of the soul because sophistic refutations or their self-contradictions are apparent since they have some logical fallacies. And I guess you relate (apparent) contradiction to (apparent) purification very closely.
I agree that the 6th division cannot belong to sophist but I have a question about the reason you gave.
Sophists are false image-maker, and they use false logoi when they want to refute others. And sometimes, two false statements can be incompatible. For example, let's consider two sentences; 'Soona is an open book.' and 'Soona is a closed book.' Of course, this is not a case of a logical contradiction for both of them are false. If, however, all people believe that 'Soona is a book.', then people would think those two sentences are logically incompatible. In this situation, sophists can assert their false logos, refute another false logos, and show contradiction successfully. But if I am right, I think it would be hard to say that sophistic refutation or contradiction is logically invalid, although it is true that their contradiction is not genuine just as you think.
And based on this point, I think we should separate purification and contradiction, although contradiction is a very important element of purification.
Unknowers, such as Socrates, can purify others' souls and it means that the knowledge of the object is not a necessary condition of doing refutation or purification. Also, purification does not mean the substitution of truth for falsity, instead, it means just an elimination of false belief, and as I stressed, one does not need to have the knowledge of the object to do this task.
So if a sophist just shows a contradiction and makes his opponents give up his false belief, then he can be a purifier.
However, in my opinion, this situation is impossible, because sophists claim that they know about the thing. They refute their opponents and make them regard the sophists' phantasma as true. As a result, the opponent's state of the soul is not changed. He still has a false belief, although the content has been changed.
In short, sophists cannot be purifiers as long as they assert they have the knowledge, inject another false belief to their opponent, and deceive it as a true one. On the other hand, Socratic refutation also uses contradiction but the task is finished with aporia and just erases interlocutors' false belief.
Thank you :-)