First I will disagree with Meditrina. There is quite a lot of difference between these schools, though much is subjective. We know plenty who are delighted with G&L often describing it at "nurturing". Others wont spot a spark and wonder about whether it is challenging enough. My guess is that if you were to pull together a group of G&L and LU girls very few would want to swap school, yet most would respect the others' choices. One is not "better" than the other, its about which feels right.
Grades and academic achievement are very important at SPGS. SPGS girls we have come across in other contexts, can often come across as unduly competitive (not all I should add!) as if this behaviour is the norm at school. There can also be a level of arrogance from both pupils and parents as if passing an exam at 11 is clear proof that they are brighter and better than their peers. In fairness though this assumption, and determination to be, the best helps produce some remarkably accomplished children and provide a sound platform for an Ivy League application.
45 mins commute is tedious but not unusual. Ask the school (when we looked round CLGS had a large chart showing where pupils came from, and I think all schools are required to provide this data as part of their school travel plan to help with transport planning). My guess is that there will be plenty of others from your post code. If so commuting can become fun, a chance to catch up with friends after school. (And annoy commuters by standing in a big gang near the exits!)
And I suspect I don't disagree with Shooting. I dont know a huge amount but have attended presentations on US applications at both my children's schools. The line as I remember is that as you are applying to a college rather than a course, there is a greater emphasis on what you have to offer, rather than your commitment to your subject. And that though EC is important requirements for overseas students are lower than they might be in the US, as overseas students tend know less about the process and because they bring useful international diversity. I think this is right, as we know plenty of straightforward, though obviously reasonably accomplished, applicants who are successful.
I would here watch for the dramatic year on year rise in applications from the UK, which may mean that entry expectations will be more stringent in a few years time.
In contrast I have witnessed some of the West London expat frenzy to fill children's schedules with useful activities. Personal triathlon coach at 9, research trip to Africa at 10.... This may be imported East Coast behaviour, and a bit over the top for London. My observation is simply that these children have parents who are well informed, normally Ivy League educated themselves. Some are very bright, others perhaps less so, but all will have pretty starry Personal Statements, and there is a lot of SAT coaching going on, starting quite early.
From what OP has said, City sounds like the school for her daughter. In 7 years time, numbers applying to the States will have increased and all these schools will have had several years more experience. If she is performing well but you have your doubts, you could always consider a move for sixth form to Westminster, ACS, SPGS or Kings Wimbledon. A lot of people use consultants. I hear some charge as much as much as £10,000, a lot, but small beer in comparison with Ivy League tuition fees.
I would also keep a weather eye out for developing your child's own interests. If she is sporty, think about sports which are taught well in the UK and popular in the US. Rowing, girl's soccer etc. If musical, look at interesting things to do. My understanding is that it is not just what you yourself achieve but how you use it. One lovely and very sporty girl started volunteered to help with disabled sport. She then realised that disabled teenagers got more enjoyment from mixing with able bodied teenagers than from the sport itself so organised for a group of her friends to join her. She was applying to the US. I hope she did well!