To give context, I was at a top academic girls school - v similar one to LEH. While I was there I was quiet and in lots of situations was very shy. But I was in sports teams, had great friends, got great grades, was nurtured through some tough life events and I look back on my time there really fondly. I see it that wherever I went, I was always going to be quiet. It was who I was and I was never made feel it was an issue, just gently encouraged and celebrated for who I was. As well, these kind of girls' private schools always have quite a few other quieter girls so I didn't feel different and I didn't need to be anyone else. The happiness that came from this kind of acceptance was powerful in itself.
I can look back now and see lots of ways the school and my parents boosted my confidence. I certainly left with a quiet confidence and huge ambition. I look back so proudly at my education and even if at the time I was not the head girl giving speeches or taking part in the school fashion show, I still loved my time there and gained so much. I always remember my parents telling me how brilliant it was that I was at that school and how proud that made them. The confidence from that in itself has stuck by me.
I remember my sister, who went to another girls' school but much smaller, less academic (similar levels to LEH Vs. ND), was forced into taking part in a debating competition aged 13. She cried and cried, was really anxious about it but the school were on a real mission to make her do it. She did it and everyone was happy, but she still is mortified by the whole experience. She had many other happier memories there and I'm sure doesn't look back with anything but good feelings about her school. She did always get referred to as 'the quiet one' as there were fewer girls and the small environment meant the other girls felt very relaxed, spoke out even more & she stood out more for not being that type. It does give an example of why smaller/'more nurturing' doesn't always equate to better for quieter types.
I think it is important to remember a school can't and shouldn't be promising to change who your child fundamentally is. Character and personality is such a natural thing that if your DD is going to be a louder, more 'out there' 16 year old, it will happen wherever she is. Equally, if she is going to become a more subdued, calm girl who has her own interests and is happy in that, then nature will take her that way. You want somewhere your DD is simply accepted and able to participate. You will get that at LEH just as much as a smaller, less academic school.
... This is my conclusions after much agony over where to send my own DC only to have them grow and change in all sorts of ways, despite the same upbringing, school etc. etc!! I hope this helps. Obviously it is just my opinion.