Before taking the private school route, come on over to Korea and look at the hagwons (private academies). It's a great system for pandering to parents, but when it comes to kids getting a solid education... Well... That rarely ends up being the best way to pander to the parents.

I know my statement isn't in regard to textbook selection or ideology pervading the classroom, but still, private school systems are NOT the way to go.

I don't know if there are enough parallels that you can really draw the conclusion that the conditions that cause failures there exist in the US.  This is particularly so when private schools, and specifically the school voucher system, have been extremely successful in the US at bringing test scores up for students in the public schools. 

It is also worthy of noting that they do it at literally a fraction of the cost. The example of the DC voucher program being an instance where expenditures per student were halved for voucher students and they saw significant test score increases.  Of course that program was cut off over the past few months despite its tremendous success...or perhaps because of it?  I'm not sure if I'm that cynical just yet, but it certainly seems suspect in the absence of some justification...but I digress.