Non-classroom duties are part of teacher’s job
Solving the problem at City Honors is simple. The prima donna teachers who are refusing to take on extra duties, as every other teacher in the city must, should do their jobs.
I was a teacher in Buffalo city high schools for almost 30 years. I taught upper level and AP courses. The students I taught were as academically proficient as the young people at City Honors. Besides teaching five classes per day, I also had study hall, lunch room, homeroom and hall monitoring duties. These duties are what the job called for. If you are really too good to do these tasks, like every other teacher, then resign and let a worthy teacher do these duties.