Allocate each child a number of prefs determined by the average prevailing wage. When a child attends a school, the prefs for all the students of a particular 'year cohort' will be pooled and distributed to the teachers, administrators, and workers involved in running the school.
Once the students move into careers, the prefs will begin earning payments for the teachers that helped teach the student.
This may imbalance education to some extent. There may be competition to teach the students that are predisposed to do well. A billionaire's son may have 6 individual instructors per year and remove the student from the general pool.
How do we combat this? Do we combat this? Teachers need to have a vested interest in their students to help assure them of success. This system may be imbalanced, but it provides for a more income and distributes economic rents more fairly among teachers than the current system.
The size of the pool of students may need to be raised to a higher level to combat the imbalance.