Yes, you often see school teachers taking upto 5-6 classes per day, however, 5-6 classes are taken up per week at university level. Teaching quality definitely will pop up. What can be done is that schools can look for trips to top-tier universities. However, the gap is bound to stay as school teachers need to feed the students, and at university level, students prefer self-learning
There are many lyceums in my town which are organized by universities. Teachers there are the university instructors. It is easier for children to enter the corresponding university when the time comes as far as they have higher level of knowledge in the subject field (in average, comparing to schoolleavers from a usual school) and they are more comfortable studying at the university because they have already got used to their instructors beforehand.
Another idea is summer or winter "schools" - short educational programs for schoolchildren organized on the basis of a particular university during school holidays. In majority of cases children enter that university when they are old enough... otherwise they know for sure that that is not their cup of tea :)