Having gone through this once with DD1 and now going through it with DD2, I can honestly say my view has changed.
I was originally of the mind that academic excellence was everything however as you go through the process, things change. DD1 was offered a s'ship @ JAGS, on s'ship waiting list @ PHS and called for s'ship interview at one of the 2nd tier GDST schools, passed all the SW London selectives and is now at TGS. She loves it, it is definitely the school for her as she also loves the sport and is very active. Is it any better than any of the other schools? On reflection and as time goes on, I think the answer is no. But is it the right school for her, definitely.
DD2 who, academically on paper, is the equal of her sister didn't pass the TGS 1st stage (although passed Nonsuch and WHSG). Having gone through the process with DD2, I now see that TGS isn't the right school for her nor is Nonsuch and WHSG and we have started to look at more indie schools for her. Visited LEH a few weeks ago, one of the top girls schools in the country. On paper, an outstanding school with amazing facilities - it is beautiful and its academic record outstanding. However, I came away from the visit feeling disappointed. I so wanted to love the school because of all that it can offer but I didn't. I can't put my finger on it but I just didn't warm to it and DD2 like the facilities but didn't like it as much as another GDST we visited with less space and is, in exam terms, lower academic record (nor did I). Consequently, we haven't applied for LEH and GDST school is now our preference.
So, what's the point of this post? Well, before I started this journey I was where the OP was - academic excellence was everything. I'm still not saying that it's not important, it is and it does have a part to play in the decision making process but I think you just have to consider each school in the round and not put any more importance on one element that another. You should also consider your DD and her personality and individual likes and dislikes. Don't write off any one school at this stage, keep an open mind and also visit as many schools as you can. You may find that you surprise yourself like I did.
Incidentally, we all loved JAGS and I was a tad disappointed when DD1 picked TGS over it (but she saved us shedloads of money so who am I to complain). I also had the same feeling about Alleyns as I did about LEH - loved it on paper and hated it after visiting.
Good luck