There is something to keep in mind about private schools that I learned in five years of coaching in them: Sure, we could recruit, but unless the family in question was loaded, it was kind of hard to say, "Hey, how about giving up that free public education to pay $4,000 a year to send your kid to our school, just because he's a good wrestler." Oddly enough, we didn't get a lot of takers.
And as Fanatic said, anyone transfering from a public to parocial school has the same eligibility rules as one who goes from one public to another.