NO. This conversation is very frustrating. Stop using other different papers. Re-read the Turing paper.
It is very clear that the aim is for the interrogator to discover the woman/computer, and that the male/human can cooperate with the interrogator.
Turing made it very clear that you repeat the game but that you replace "woman" with "computer". It is impossible to do this without telling the interrergator that they are playing against a computer.
You keep saying that Turing did not explicitly say that the human should be made aware of the computer. But he did say that - by repeating the game but substituting "computer" for "female" you inform the interrogator the same way in both games. In the first tame you say "spot the woman" and in the second game you say "spot the computer". Unless you're saying that you don't tell the interrogator that one of the talkers is a woman.
Here, again, is the quote:
Your quoted error above makes me think that you have mot recently read Turing's paper and so I won't waste any more time discussing it.