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.
Yes, I think private scholarships and aid would work fine, as they have for decades in colleges. Also, even renters should realize savings from property tax reductions, since apartment owners' costs would be reduced. And of course everyone benefits if sales taxes and/or local income taxes are cut (the amount depending on the State).