The idea that you can reduce the body count of school shootings to a "manageable" level is a concept I don't really understand. How do you define manageable? Is one massacre a year manageable? How many innocent students can be killed and the number still be considered manageable?
It's no different from any other approach to crime. Is one death per year caused by a drunk driver manageable? Most people would cheer that result.
You're talking about massacres. If teachers are armed, the likelihood of any massacres will probably be much reduced. I'd say one massacre per year is better than two, and much better than three, four, five, etc. I'd say one non-massacre per year - where one or two people are killed before the shooter is downed - is better than one full massacre where ten or more people are killed.
And it isn't just kids doing the shooting. The granddaddy of school shootings was the nut who used an AK-47 against kids at a school in California. And then there was the adult man who shot up the Jewish school in California.
Armed teachers can help mitigate both scenarios. They would even be helpful if terrorists began attacking our schools.
Personally I don't think the Columbine shooters or the VT shooter would have been deterred by the presence of guns in the hands of teachers and/or students. They knew when they started they were going to die before it was all over.
They also knew, and revelled in the knowledge, that they would take many lives first. If an armed teacher could have saved even one life, that's a good thing.
elimination of school shooting
Unless you intend to run schools as maximum security prisons, you will never achieve total elimination. Even max security prisons have problems with violence. Again, if you are seeking perfection, you are not seeking a solution because you are not living in the real world. I doubt the OP was seeking perfection.
But again, WHAT IS
YOUR SOLUTION? You never offer one; you simply snipe at others.