Perhaps a simple change could be to have sections. Of course this does little to convey what I was really thinking.
I would suggest a long school day 8am to 5pm. But it would require full time and part time teachers. Full time could go from 8-3 as usual, and part time could teach in 2 shifts (say 3-4 hours per day). This would allow more sections to be taught by more than one teacher at different times during the day. I do not assume that all kids go to school at the same time. some may have the typical schedule and others may have a later, lagged schedule. This probably only "works" for high school ... until you consider sports and other "after" school activities, of which teachers are an important part.
Imagine what schools would look like if they could both hold more students and teach more classes. If a student is having trouble, you suddenly have options like different teachers or a different time of day. Or they sit through the same lecture again to help them understand. Perhaps less students would end up in each class and get more time from teachers. Less students may spark more motivation to learn and allow teachers with a passion for teaching to teach at a high level without being drowned in students and homework.
I read an excellent blog post from a teacher today about rules. I enjoyed this quote: