By putting a "Lock-key" Police Sub-Station in each school, the appropriate local, county, and & state police could come to the school during school hours to complete reports, et al. By doing so you would have the benefit of an intermittent, varying number of police, on-site at any time. This uncertainty would add to the deterrent, just as gas stations offer free coffee to police. You never know when another cop is going to walk through the door.
All the cost would be is a room, the number of keys for police, computers (remote networked into the various police systems needed).
This would put Law Enforcement onto school grounds without taking away from their other responsibilities to the community.