squeak, Is it really realistic to expect you can set a flat per child tuition rate that 75% can comfortably afford and another 12.5% can meet with straining? Right now most people are straining and perhaps 12.5% can comfortably afford. To achieve your objective, you will have the seemingly (to me) impossible task of setting such a tuition rate.
And if the family’s sincere attempt to directly solicit funds is unsuccessful (i.e. during hard economic times), will the children be thrown out of Yeshiva to the streets or PS? If not (and it is obvious that not), you are (at least partially) back to where you started.