Why didn't they just kidnap Aya from the beginning if the whole point of Platonic Heart was to submit Aya to the same treatment Miko and Natsume's mother got? Does creating a "perfect woman" not work if she hasn't been stripped naked while having the snot beaten out of her? Perhaps this is a product of Revenge Before Reason and Best Served Cold.
More likely? This series was just lazy and terribly written.
That too, but then the "revenge" was to A. Completely break Aya's spirit (no one loves you, guilt at what you've helped accomplish, you are a monster/child of monsters), B. Torture and brutally MURDER aya (not sell her), C. Let Aya's mom know they won, then kill HER as well. So the insane complexity does make some sense. if only in a stupid melodramatic way.
First, Aya is far stronger than Natsume, Miko, or Harumi. Heck she took out an entire school all by herself. It's far more practical to trick her into going into this mess voluntarily. Second, if Aya had lost and been sold into sex-slavery, Aya's mother would have been hard pressed to do something about it.
Is the tournament real or not? The simple answer is no, they made it up for torture reasons, but the double's lines, as well as some of the other characters suggest that it just already happens, and that the three kids hijacked it for their own purpose.
The final lines of Aya's mother (and the fact that she got a cell phone text after killing Aya's "friends") leads the audience to believe that the tournament is still ongoing, and the organization is far larger than what we've been shown.