These are tough times for Catholic schools. I am sure you remember the travails that lead to the closing of the school in Diocese of Madison (HERE). Any number of schools are struggling.
I had an email today from someone at a pre-K-12 Catholic prep school in Lafayette, Louisiana called the John Paul the Great Academy. (I don’t want here discussion of whether or not Bl. John Paul should be called “the Great.) The school apparently used a form of the trivium et quadrivium and also has 24-hour adoration of the Blessed Sacrament.
It seems they are on the ropes right now. You might consider looking at their website.