You don't need official "participation."
Just remove the "gun free zone" shackle from schools which will allow teachers who want to carry to do so.
Which is what I had just said to you. But most people are taking the simplistic view that simply relying on teachers' view of their own defense will willy-nilly protect their charges. This is not a plan for those whose specified responsibility it is to guard against sociopaths, even from within the body of teachers and students and janitors, etc
Your (lack of a) plan simply leaves too much up to chance and does not account for the myriad of legitimate objections to it. I would not like my security and living as a professional educator or administrator left in your hands, to say frankly.