coach time shouldn't be seen as 'lost' time as they end up socialising a lot and the girls don't really dread it.
This is true for most girls. From where you must live, there should be several girls in your DD's year on the same bus.
In the morning you'll have to leave home around 7:35 to catch the NLCS coach. What time would you have to leave home for SHHS? 8:25? Which is more convenient for your family's schedule?
don’t underestimate the hassle for you when it comes to parents evenings, school events, location of DD’s friends.
NLCS will ask you to come by at least 2-3 times a term. In year 3, I'd expect only 4-5 birthday parties a term, but likely more inconveniently located for you than with a SHHS class. NLCS's catchment area is quite large, even in the Junior School. I suspect that SHHS's is not as large, but ask your friends there how many girls really live locally.
You won't be able to do any 4pm activities around Hampstead. Your scheduled drop off in the afternoon will be 4:22, and that bus usually runs late, so 5pm is the earliest realistic time slot.
I’d take SHHS and move at 11 if you feel your DD needs more.
That might be easier said than done, from either school. Afaik, neither NLCS nor SHHS spend much resources preparing their junior school girls for the 11+ process. If you want or need to change at that point, you're going to have to do a lot of preparation yourself.
Wouldnt any reasonably bright girl do equally well on both academically anyway
This is a point of tremendous contention.
(maybe it just happens that NLCS has a larger portion of even brighter girls)?
I have direct knowledge of only one of the schools, so I can't compare. That said, I have no reason to believe it; I'm skeptical about how accurately schools can evaluate the ability of 3 year olds. I do, however, suspect that the average NLCS parent might value academic achievement a bit more highly than the average SHHS parent. However, this belief is also controversial.