I sent my older DD (now 25) to a Lutheran school, although I am religious I am not Lutheran and I did not go to the church there. I was a divorced mom on little income and they worked with me on the costs to make sure she could go. Also, later when she entered public school in 5th grade she was a good 3 years ahead of her classmates, I say this because even though she is bright I don't know if I would say gifted.
I think the bottom line is the school will welcome you, help you with finances if needed, my guess is that they would more than likely work with you on DD school work if needed, even if you send your child there for a year and then go to a public school. That's just what most church affiliated schools do. Good luck and best wishes
