Japanese are natural collectivists. You cannot break any one of them individually, but you can break them by making them feel like they've let down the group and betrayed their belief in them.
I propose that since Tayleigh is broken and pathetic right now (but not in any real danger to herself and others), that Shinji be given a task to save her from elimination, one that's essentially impossible to do (but it must seem possible but difficult on it's face). When he inevitably fails and she has to leave complete with teary goodbyes, that will rattle him more than anything they can do to himself.
You listening to this, Goran? I'm handing it to you on a silver platter, free of charge!