If we could eliminate Federal, state and local government from the education business altogether, our taxes would be cut dramatically. Local and state by 50%. So then the education consumers (parents, students) would have the CASH in their pockets to make choices without any government voucher system at all.
A starting point would be offering your county's school "business" to private education companies. (This industry would grow fast.) They take over and bill parents. Sell school buildings to either the education company or other investors, with lease back to education company. Eliminate county and state school-related taxes, which are huge part of current real estate tax bills. Cut sales taxes, get rid of all government employees associated with these schools. (Many would probably get jobs with private companies.) An example of this is already happening, in part, as Kelly Education Services takes over substitute teacher "business" in my area.
Those are some excellent proposals. I read recently that our county's school system absorbs over 60% of all county tax expenditures.
I don't think tax reductions would make private education affordable for absolutely everyone, but certainly for most. For the poorest, churches and private scholarships could pay. For example, there was an interesting article recently about how the Diocese of Wichita offers tuition-free Catholic schools to every active Catholic family in the diocese.