re: wealth being redistributed down.
That's pretty much the only way it does get redistributed. If you think about it, redistributing wealth from people who don't have wealth is not easy to do.
Not to put too fine a point on it, but your major objection about vouchers serving the rich is largely mythological.
I also addressed your objection to government money going to private and even religious institutions by pointing out that this is done all the time in higher education.