I don't think I missed anything.
There can be only "god-centered" or "godless", neither of which are "god-neutral", so there is not and can be no "god-neutral". "Godless" is the same as "atheist" so everywhere you see the word "secular" you should scratch it out and replace it with "atheist".
Exactly! It is for this reason that education is never religiously neutral. Government should begin getting out of the education business.