Yes, I know a lot of girls who go or have gone to LSU, going back to my oldest child's cohort who are now turning 20, and including at least 20 girls who will be starting in next year's Y7. It's the main destination school for most of the catholic primary schools in North London, and virtually all the girls from my sons' primary school classes have gone there.
Bright girls do as well there as they would anywhere, and averagely bright girls seem to be well-supported, as do girls with social and emotional issues. There's a good mix of girls from different backgrounds, plenty of middle-class families included. Fabulous location just opposite the Heath, and lots of lovely greenery within the school grounds, including an orchard and the Catholic-school-ubiquitous prayer garden.
It's not a school that would suit a determined rebel or rule-breaker, but that's the case for all the schools on your list, so presumably you're okay with that. The head is lovely, and there are lots of dynamic teachers.
You are unusual in mixing CofE schools and Catholic ones - most people who want their dc to go to LSU or Sacred Heart would be only or mainly looking at RC schools and putting others as backup, so would have a bit more of a connection to the schools and know other families applying, as well as dc already there. It's quite hard to see how you could fulfil the admissions criteria for both GCH and LSU tbh, given the religious practice requirements and the fact that most of the schools also have a distance criterion somewhere in the small print.