IMHO trained School Marshalls or special Sheriff deputies are the only answer...
I appreciate where you are coming from, but I’d like to keep this from adding more paid staff positions that could form a union and become a major pain in the ass. I also don’t want to see our education system burdened further by top salaries for positions that can easily be filled by volunteers.
A self vetting association of volunteers would fill the bill nicely IMO.
Thinking back on my HS days (1970-73), I can remember one Biology teacher that certainly fit that description. He was one of my customers on my paper route, too -- hated going to collect there. He'd probably qualify for the Asperger's label today.
The price of that stops it in most city budgets these days - and the liberals cry for total disarming of the public (a stupid idea that will never happen.)
And, yes, I know several teachers who are indeed 'a couple of bricks shy of a load' - frightened to death at even the sight of a gun.
So perhaps in some places volunteering retired police, sheriffs, etc. might be a logical alternative, as mentioned above.