The plan goes like this: the distraction squad will put on a rock concert, then, at the height of the concert, they'll activate a giant fan, blowing all the lunch tickets in the cafeteria out where they can grab them.
All Otonashi has to do is hold off Angel.
Too bad she's invincible. When she comes up against him, she can parry his bullets. When the others back him up, she activates a shield that deflects them.
They buy enough time for the operation, but deal basically no damage to Angel.