Budgie you have already answered your own question - I did a very similar job a few years ago.
Whilst the problem persists the kids will have to eat indoors, because when the food stops being available the birds will stop bothering the kids. It will be a pain for the school, but its the only way as you won't get a Licence for any type of lethal control.
No food on the yard, no food left behind, good housekeeping and the problem will go away, although it will take time.