I see a common practice of posting a comment that diverts the exact focus of the OP. While I generally do not like this, I will follow the lead.
The frum community has more forms of tzedokoh than can be imagined. Peruse the gemach list in the frum phone directories. It is staggering. there are many other versions of charity that boggle the mind. There is one that I have yet to encounter (though I have heard it proposed several times).
A tuition fund. Yes, people donate funds to assist parents in paying tuition costs. These funds might be channeled away from the yeshivos fund raising efforts, but the money ends up going to support the yeshivos. Meanwhile, some parents will not have to face the threat of not allowing children entry to school.
The picture I have of this is that it is based purely on hardship. I cannot rate the forms of hardship, but it would include single mothers, parents who are unemployed or lost jobs, those with medical expenses that drain them, and even those who work but are underearning. Disqualifiers can include taking trips for vacations to E”Y or elsewhere, having luxury cars, making lavish simchos, etc., all indicators of hardship just being priorities that are unfair to the chiyuv to provide chinuch to one’s children.
Obviously, the panel of evaluators would be broad and inquisitive. I envision such a fund holding huge fund raising events, ones that rival some of the greatest ones in our community. The tuition burden is so overwhelming to so many, and it would be just and right to create a mechanism to ease such pain.
One fear – yeshivos won’t like it.