LEH OR G&L

Honestly you're fretting about minute differences between two excellent schools - either will do very well by your dd

The music at LEH is absolutely first class so if your dd is a musician that's a massive factor in its favour

G&L is not much more selective than LEH - I'd have thought both would have an intellectually similar cohort, just slightly below St Paul's

If she's still set on the IB later she can go to a number of schools which offer it - the numbers taking it at G&L are pretty small at the moment which might mean that some subjects will only have a couple of girls in a set which isn't much fun as there's no one to bounce ideas off

It would be madness to turn down a music scholarship at a closer school in favour of full fees elsewhere unless your other option offered something much much better which simply isn't the case here

Premature post...
Your reasons for preferring leh seem slightly based on supposition and perception. Personally I don't take much notice of league tables as a bright child in any of the top selectives will perform well but leh is consistently one of the top performing schools so the 'easier' paper is an absolute red herring. These schools take the top performing children, an 'easier' paper doesn't mean a less intelligent cohort. The top performing children are offered the places. I've heard that kgs was one of the hardest papers this year.
You have to ask yourself how much more you prefer gl to leh and is your perceived preference to the added value of gl worth the extra travelling time.
Also, why is a more central London school going to be better? Because if you're going for what you think is the 'best' I would argue that there are a number of 'better' London schools.
Personally I even think considering 3 changes is crazy. You say your daughter is willing to do that because she likes the school. Does she love it that much more than the closer school or do you?

It's s balancing act. 3 stops against what is your clear preference for g&l. My daughters are at leh and they love it. The eldest opted for it over St pauls. Your reasons seem

3 trains is not an option

god no .. 3 trains is way too tricky a journey - it would be a hideous commute for an adult and make extra-curricular stuff tricky

It might be just about feasible, though exhausting, when all transport links are working perfectly, but stressful beyond belief when (not if) something goes wrong

I had a horrible bus then train journey for my first two terms at G&L aeons ago but we were always going to move closer in and that made it bearable

You could always suggest that your dd moves to an IB school for sixth form

Hmm, how long is the journey? A music scholarship is usually not a lot of money, although I don't really know for LEH, and has a lot of strings attached, i.e. she will be expected to perform for every school event. Is it possible to go and visit the schools again?

G&L offers IB. Would this appeal?

They are two great schools, congratulations to your DD. We had the same choice for our DD a few years ago and went with G&L. It just felt a more vibrant, intellectually curious school that produced true citizens of the world. Girls who went on to lead fulfilling lives and also put something back into society. We remain very happy with the school, as does our DD.

LEH however felt like just a big country club, isolated and insular. But that is just our view. Other people we know view it very differently and their DD are very happy there too.

Which is easier to get to? Does the music scholarship make a significant difference to the cost?