You are forgetting the most important element of your scenario,the teachers union and the ability for towns to pay for the salaries of additional workforce to handle those extra hours. Heck this is what is going on in some local communities here just north of Boston.
Stoneham: Threatening to cancel ALL Varsity sports
Winchester: Huge fees families pay for sports participation
Lexington: $550/ Student to take a school bus,staff layoffs
Etc.... You get the point. IMHO cut the police and fire budgets(positions) in these communities. Bloated as far as I can see based on level of crime and need for fire services.