Ok. First off, girls go to senior school at 11 not 13 like boys, so their tolerance for long journeys to school is much less. So you need to narrow your distance range if you want your daughter to have the energy to make the most of her time there and extra curricular opportunities in particular.
Second, because of this, girls generally travel less far to their schools so for friendships you want to be closer to the school. Only exceptionally good schools will have girls traveling long distances and most on your list are not exceptional.
Third if you are sending your DS to one of the country's top boarding schools, from a feminist perspective I seriously hope you will make the same investment in your DD. If he deserves private school so does she.
Then I don't think you had any boarding schools on your list - why not?
So if your DD is this bright you should be looking at a small selection of schools only and will be wasting your time with others. So SPGS, CLSG, G&L, HBS on the day school front. For coed day Highgate. And boarding - if your DS is going to Harrow you should look at Wycombe Abbey at least.
And yes to the advice to work on her resilience and tolerance of failure...but as a perfectionist myself I found a girls school where I could excel a very comfortable environment. A mixed school would have been too stressful.