Wolf, out of curiosity, if the problem is only the State’s inability to pay anything to a facility that teaches religious studies, then why not (at least for the higher grades, say 6+) have the Yeshiva portion of the education take place in local shuls, and then have the Yeshivos teach only secular studies in their buildings and be fully funded by the State?
The problem with your suggestion is that the same rules apply if the school is under the control of a religious organization, even if religion isn’t taught in the school. So you can’t have a yeshiva split into a “Hebrew School” and a “Secular School” (and have the latter funded by the state) because the Secular School would still be under the control of the religious school/organization. You could, if you wanted to, remove that control, but then you’re opening up the possibility of your kids sitting next to the same people I mentioned above — which would never fly in New York.
The Wolf