According to the St. Anthony Academy website it is Classical Latin School Association (CLSA) Accredited. www.stanthonyacademy.org/
I don't have any information about the other schools. But I would be interested in learning more about them.
St. Anthony's looks like a great school, and its not far from St. Athanasius Church, but let's face it, Northern Virginia is one of the most expensive places to live in the entire country. So I am hoping that someone here can share more info about the school in Texas and/or New York/Connecticut.
I am really just in the information gathering phase since my wife is a long way from coming along to tradition. I am trying to lead by example, prayer, and with God's grace, a meeting with one of the priests or bishops to allow her to talk with one of them about questions she might have. (It should be said, that God has answered that prayer in a miraculous way and a meeting is in the works for August).
I could email one of the priests or bishops to ask them about these schools, but I know how incredibly busy they are.
I am blessed to be surrounded by some incredible people in tradition that are supporting me and guiding me and my little family. It is truly by God's Divine Providence that I have been led from the clutches of the Novus Ordo. Pray for my family dear brothers and sisters. Prayer for my wife that she gains the eyes to see. Know that we are praying for all of you!
Kyrie eleison. Christe eleison.