Perhaps lessons can be taken from other places around the world which dont seem to have this problem with the same horrific regularity you see here. (I'm talking modern 1st world democracies here, not 3rd world, perpetually-war-torn shitholes. That would be comparing apples to oranges.)
Maybe it's worth swallowing some pride, taking a long hard look at why nobody in Australia or Canada or England, etc. is calling for their teachers to be armed to protect their students, under the premise that it is simply a matter of time before an armed wacko inevitably enters their campus and shoots at people. These places all have more strict gun laws. Maybe something can be learned from them ?
Some suggest that stricter gun laws leads to only the "bad guys" having guns, thus worsening the situation, since the crazies would know there is no threat of return fire, so would be emboldened to commit such acts even more frequently, and with more devastating outcomes. And yet, as logically sound as that premise admittedly is, their predicted scenario does not seem to actually manifest itself elsewhere.
If you could prove the premise that mass shootings (or attempts at such mass shootings) are truly inevitable/unavoidable, then giving the innocent law-abiding people some method to mitigate the "almost-certain" future damage seems to make some sense, so you'd want to loosen, not tighten, the gun laws. It would deter would-be shooters, if they thought Miss Jones in grade 3 had a 9mm in her desk and knew how to use it, or so goes the logic.
However, nutjobs in Sydney, or Toronto, or London dont seem to be storming their campuses every couple years, and it certainly cant be due to any deterrent created by armed teachers, because those places dont have armed teachers. Many times I've seen on this board the expression, "an armed society is a polite society". Look around, other places are polite, peaceful societies too, and nobody there is armed.
I'm not saying I have all the answers, these are just some thoughts and observations...