Hi
I just saw this, don't know if you're still looking for info. I too am in N1.
My daughter is at SHHS, she started last year at age 7. It is fabulous and I am more than delighted with it. She is stimulated and having so much fun but not being worked like a dog which some of the schools do I think. It's got good facilities, better than most you list and these are set to improve further as the Senior School has been given planning permission to be substantially rebuilt/updated etc. The junior school use quite a few of the senior schools facilities.
I looked at St Christopher's and liked it a lot, it was my second choice. SHHS was my first as it has better facilities, particularly for sport and avoids the 11+ exam which I think is pretty awful.
I know people at Charterhouse and they like it but the kids do work very hard as they are aiming for City of London Girls School so homework every night at age 5...
I don't know the others. I know a woman with 2 at Channing and they like it. NLCS is a long way and not really connected by transport and the nearest their buses come is Muswell Hill. I know people who send kids to Lyceum and they like it, heard nothing bad other than it is a very urban school with maybe no outdoor space, not sure though on this.
You have not put The Children's House on your list. It is N1 and is absolutely fabulous they have a nursery and then a separate building that goes through to Year 2/ age 7 then the kids take tests to go into their next school. It avoids the schlep of school runs for a few years and they get to make local friends and it really is a great school, amazing outstanding OFSTED etc. You generally have to register quite early eg by the age of 1, but if you like it I'd register straight away and hope a place comes up, they often do. The nursery starts at 2 and a half, they do short half days.
Also The Cavendish in Camden, Highgate and St Paul's which N1 families travel to. The Overground serves the Cavendish and SHHS.
In short there are a few options you can travel to, and they are all good.
Good luck.