“Taxpayers do not have a right, nor should they have a right, to determine how private schools spend money to educate children, even if partially tax funded. “
Actually, taxpayers DO have such a right. You take government money you accept government strings.
And if such a plan as you suggest ever becomes law, you know very well that some Jewish head of school who pretends to be Orthodox will improperly spend the money and there will be a massive Chilul HaShem.
It should also be noted that the government has the right to regulate private schools even when there is no funding because education is something necessary for the good of society. That was established in Judaism back when the Temple was still standing! New York State has regulated private schools since 1784.