“I think the biggest obstacle to this solution is the pupil in question and his/her parents themselves. They don’t want to go there.”
I agree. It’s mainly the responsibility of the parents to get their child into a new yeshiva, not the old yeshivas’. If they would move quickly to get into the MO yeshiva, 9 times out of 10, the kid would be accepted. If they dawdle and fight the old yeshiva or try similar types of “Ultra-frum” yeshivos, they most likely won’t be successful and the kid is “Meyiish”(gives up). After this, it becomes very easy for him to go OTD! The parents have to take their ego out of the equation. Right or wrong, accept the Yeshiva’s decision and move on. Fighting city hall doesn’t work. I don’t mean that you can’t try to speak with them or have s/1 intervene on your behalf, but if this doesn’t work, send the kid to a MO yeshiva!