I think that Kyouko decided to give Manabi chance after talking this over with Takefumi. There was a shot where she’s shown pondering his revelations about Manami’s previous life and relations to schools. However, she did not want to spoil Manami. She also used this occasion to ground Manami in reality a little bit (that other people have other priorities, and Manami has to take that into account).

Realistically speaking, 70% is never achievable under the circumstances. You have to have a Soviet-like system to get that many people to sign any petitions. It is an insurmountable hurdle. Since I follow raws, I know that it was indeed insurmountable under normal circumstances, but… you’ll see how it goes in due time. But I continue to think Kyouko did not actually set Manami to fail. She simply made a poor judgement call on it.