Cut it back enough to put up railings or a rail then let the hedge grow
into the railings. You could brace the railings from within the hedge
to give extra stability. Kids won't be jumping into a railing for fun.

That might solve half the problem, but add to the other half... that of them
throwing other kids into the hedge?

They push each other into it rather than throw each other into it, and
I think that there would be no 'fun' in doing this if there was a rail.