I hope you have deep enough pockets. The religious schools always discount well for 'belief', they already know they can guilt you into more $$$.
The more secular alternatives thus cost more, but you get more, like real science.
My two kids each went 13 yrs to Trinity Valley School in SW Fort Worth and it is secular, and multicultural. Also a great school in SW Fort Worth is Country Day. I don't know about FWCD, but TVS has long had a bus run from Southlake/Collyville.
Almost all other private schools I know of are religious.
Both have good academics. I'm partial to TVS of course, but it's a long way from your intended move direction. Check the schools against National Merit honors and see what you think.
Good luck, glad to help more if I can.
I don't know a lot about Greenhill School in Addison but I didn't find any religious references on their web site, they have a good reputation as far as I know.
Yes there are options, and it is good to start the search for information before the move. The options available also depend upon the age of the kids, and their personalities/learning styles.
Harmony Science Academy is a good option if you could get your kids into it. It's a charter school so you wouldn't have to pay anything, you just have to get the kids accepted and live in the right area.