WCM - Good luck with your move.
I recently did what you are doing but in reverse and for a much shorter time (I was in the US for 6 months a year ago now, not a million miles away from the Windy City, in fact!).
My dd1 was in 5th Grade over there and in Year 6 here, so I can confirm that 6th Grade = Year 7.
Much depends on the child, I think, as to how well they settle. My dd1 was a bit unsettled by the move, whereas dd2 just fitted right in and after a week it was as if she'd been an American girl her whole life. (She was in 3rd Grade btw.) On balance, though, I'd look for a solution where your dd doesn't have to change schools halfway through her time here. That'll give her the chance to make lasting friendships and to feel properly settled.
Just to say that often religious schools here are quite 'light touch' compared to the US. I am not a Catholic, but because I was in the US for a short time I couldn't access the public school system (even if I'd wanted to) and most of the private schools where I was were Catholic, so the dds ended up in a Catholic school. It was a lovely school and everyone was really kind to us, but the religious aspect was quite - how to put it? - full on (Mass three times a week, prayer services on the other days, prayers after every lesson, something called 'liturgical singing' which I never really fathomed, etc etc.). I am not complaining, because I knew what to expect, but this was just to say that a CofE school here might well be limited to a prayer in the morning and the occasional church service (e.g. at the end of term), so could be quite different from a religious school in the US. (Though maybe the one I ended up in wasn't typical - I'm not 100% sure.)
My other piece of advice would be just to phone the school you're interested in and talk to them. I chose my US school on the basis of the welcome I got when I called them and explained our circumstances.
Wishing you the very best of luck.