If sheriffs are not so snobbish and departments are not so unionized as to prevent this.
Nearby, Washington, Illinois has done just that, getting around Illinois' lack of concealed carry at the same time. The school board asked for teacher and administrator volunteers to go through police training and with the cooperation of the local police force, they have had no lack of volunteers.
When they are finished with the training they become police officers/teachers. All of Illinois is not dumb ass liberal Chicago.