As a school, each of these proposed schools will be some of the most expensive ones ever built, at least among schools at the pre-primary, primary, and secondary levels. Each school would have to be designed to entice even the most reluctant parents - from those who qualify as being politically influential - regardless of whether they can contribute some tuition.
As a conflict-resolution option, however, these proposed schools will be inexpensive, relative to other conflict-resolution efforts that include military costs to maintain the status quo, such as on the Korean peninsula, in Afghanistan to hold off the Taliban, in the mountains of Kashmir between India and Pakistan, and on Israel's borders. 1% of the military and conflict-resolution budgets for the conflicts listed on this website should be given to The Cypriot School as a research-and-development expense. This is because if The Cypriot School leads to a solution in Cyprus, then this type of school could be replicated in these other conflcts, and if successful there too, it would bring a massive decrease in the amount of money currently being spent in these places.
Regarding tuition, The Cypriot School should not be completely free, lest parents justify sending their child to the school simply because of this. That would negate the cognitive dissonance that we need parents to feel in order for them to want to change their attitude about the other group over time. If they have an external justification in enrolling their child (free tuition!), they won't have to internally justify it, and the need for internal justification is what creates cognitive dissonance with the discordant attitude.
Perhaps the best tuition strategy is one where parents
1) are asked to pay what they think their child's education at this school is worth; 2) write in a permanently confidential document - observed by a impartial observer - this amount (but not pay it); 3) pay what they can actually afford; and 4) are asked to volunteer at the school for at a couple of hours per year.