If you have a strong preference for co-ed, then you might have a clear first choice. As for the girls schools, while I agree that all three are in the same league academically, I don't agree that they are practically identical. For example, my recollection is that when we looked at the numbers, we found that a much larger fraction of girls took STEM subjects at A Level at CLSG than at SHHS, with G&LS in between. Also, G&LS offers the IB at 6th Form which none of the other schools do.
As for non-academic issues, I very much agree that friendship groups are mostly a matter of luck. However, there are other relevant considerations. When we spoke with the girls at the open days, we came away with the impression that CLSG had the largest effective catchment area, with many girls taking the tube for an hour (or more!) from all points of the compass, whereas most girls at SHHS lived far more locally and G&LS in between. This can make a difference for how easy it is for your DD to meet up with other girls on weekends to form and sustain strong friendships.
As for "fit", our considerations included how much the schools engaged with DD's interests, and there were major differences. As an example, we came away with the impression that a girl who wanted to do a lot of sport might prefer G&LS to CLSG. G&LS just seemed to do more of it and have more teams than CLSG, besides the differences in facilities.
Finally, at the open days, it was clear that the schools had substantially different mixes of ethnic and national origins. SHHS was the most white and British and CLSG the least of each. Furthermore, while it wasn't visibly obvious, we certainly had the impression that CLSG was more economically diverse than either SHHS or G&LS, with a larger fraction of girls coming from state primaries as well as a larger fraction of girls on bursaries.
It's up to you how much you care about these various differences and, if so, which you prefer; but they do exist, or at least we thought that they did three years ago.