"The reformer is always right about what is wrong. He is generally wrong about what is right." - G.K. Chesterton
I couldn't attempt a solution without Chesterton's help. I'm certain that he would agree with me about the condition of the Catholic schools, though he would be far more optimistic about them than I am; and I further believe that he would agree with many of the solutions that I shall attempt to offer herein, though I rather think he would humbly protest that there are far better things for people to read than any of his books.
The solution, as I see it, is twofold. First, teachers at Catholic schools have to be Catholics; the more sincere, the better. Now, it's not imperative that the math teacher can quote Chesterton, although a certain quip about triangles comes to mind which would delight many a math teacher; but they should have a basic grasp on their faith, as all adults should. More importantly, they should have that personal relationship with Christ without which are faith is null, and which produces the love which is often a better witness for the Gospel than the most well-written apologetic.
Second, the teachers should have a good idea about what the Church thinks concerning their particular field of study. This presents an impressive task for the religion teachers especially, but hardly an insurmountable one. While it is impossible to read everything ever written by Catholics, to say nothing of the wonderful writings of the pre-Catholic pagans and Jews, and the many partially good things written by non-Catholics, especially in the years since the Reformation, it is very possible to attain a good grasp of the matter. A religion teacher may not have read all of, say, Newman, but one would hope she would have heard of him; he can be forgiven for being unable to get through The Summa, but he had better have heard of St. Thomas Aquinas.
The problem with the former has been touched on already. Sanctity is far too scarce in this fallen world. As to the latter, I believe that the reason our teachers didn't touch on the Catholic giants of the past is that they were honestly unaware of them. Poorly educated people make even poorer teachers; the cycle of mis-education is self-perpetuating.
The solution, then, involves people who received good Catholic educations, or autodidacts like myself, should try to give back, becoming teachers in the Catholic schools--and before you ask, yes, I'm considering it. One more mediocre teacher isn't going to do much to degrade an already bad situation, but one good teacher can help immensely. Once one has heard of, say, Hopkins, one isn't likely to forget about him.
Which leads me, quite readily, into another point: Catholic teaching should in no ways be confined to religion classes. There is no reason the English classes--to take only one example--shouldn't similarly provide an immersion in Catholicism. As Mark Judge points out in God and Man at Georgetown Prep:
"The Catcher in the Rye is indeed a wonderful book, and I have no criticism of its inclusion in any high school curriculum. What I now find disturbing is that the book was not balanced by a curriculum that included great Catholic books--The Man Who Was Thursday by Chesterton, the space trilogy by C.S. Lewis, Brideshead Revisited by Evelyn Waugh. From The Catcher in the Rye we went not to Tolkien's Lord of the Rings but to Lord of the Flies, another book about juvenile delinquency." p.63
I personally think The Catcher and the Rye, which we also read, is overrated, and it's a bit unfair to lump Lewis with the Catholics, but Judge's suggestion is worthy of a hearty second. Brideshead Revisited is an amazing novel, and it is a shame it is not read oftener, especially among Catholics.
The word catholic means universal; far from entering a smaller world, the Catholic universe is exquisitely rich and inexhaustibly large. In fact, the difficulty in composing a curriculum for Catholic schools, is not in figuring out how to plug a few Catholics into it, but in deciding on which authors to pick and how much room to leave for non-Catholics. Glancing at my bookshelf, I notice a large number of books written by Catholics--no surprise there. But if anyone would suggest that this has narrowed me, I need but hand them a reading list. You may think all sorts of things about the Catholic Church, but it really is "the only type of Christianity that really contains every type of man; even the respectable man", to quote Chesterton, and nowhere is this more obvious than in a survey of the various Catholic men--and women--of letters from the last two millennium. Any church big enough to contain Hilaire Belloc and Oscar Wilde is an impressive church indeed.
I thought about ending this with a recommended reading list of sorts, composed by myself. But Fr. John McCloskey has outdone me. And thank goodness, too. Any list I composed would be far too short. Catholic schooling is only the beginning, for as Fr. John points out, the reading list should last a lifetime. Upon finishing, one would hardly have begun to mine the rich treasures of the Catholic Church, and come no nearer to plumbing the infinite mysteries of God. Ultimately, it is too God that such an education should point, and it is a task of tremendous worth to point the young in His direction. As always, the harvest is many, but the laborers are few. May the master send more laborers for the harvest.