My kids attend one of the schools you mentioned, L&B. I would very happily recommend the school, including the ELC which is incredible. I will PM you when I get a chance - need to settle the kids and am working tomorrow, PM me if I forget! I have also looked at all of the others you mentioned.

You will find that all the independent schools in the Bayside area have an affiliation to a church (all independent schools, I think, not just Bayside!). Some are more religious than others and that's something to research and consider when looking at each school. None of the schools you have mentioned are fundamentalist, but each will have a component of religious education.