I would personally find it very hard to reject an excellent and local state secondary. But it is definitely worth getting to know several independent schools, and then, at the very end of the process (when your view of them will be clearer, and you see which schools come through as offers or waiting lists worth waiting on - then you make the choice - as it appears you are doing/planning.
In our case (2 years ago) the choice was easier - it was between a very mediocre state school and an independent we believed was a great fit for our DD. That fit appeared quite clear (at the end of the long process) not only because it was at the right academic level (academic without being scarily so) and especially after seeing her smile every time she went to that school (open day, test, interview etc).
DD had been coasting and hiding (keeping her head down) in an OK state primary - with little homework, so-so teaching and some low level disruption. The state secondary appeared to have a somewhat similar culture to her primary, and knowing DD, she would have taken the same approach as at primary, and keeping many of the same friends. We wanted a friendly, supportive and academic school where she would be comfortable and hopefully gradually grow in confidence and be encouraged ("pulled") to work and achieve more than she did at primary.
She was similar academically to what your DD sounds like, OP. BTW DD also loved G&L, but that was always a (too) long shot.
Now (in year 8) she is thriving, working hard at her homework (without any pushing), with good new friends who are a really positive and friendly peer group - and really excellent teachers. She is proud of her school and keen to keep up. Occasional positive reinforcements (merits for a good test / homework piece, or a good comment in class) really works a treat with her. She is noticed (but still keeps a modest profile, as is her personality) and also likes (almost) all her teachers and also the SLT, who seem very approachable and warm - so we appear to have achieved what we had been hoping for.
Whether your DD would respond similarly positively at independent X (relative to W) is of course a key question.
Grade speculation/expectations are tricky and might come back and bite me in a few years, but in my DD's case, If you force me to bet today, I would say she is likely to get mostly As with perhaps a couple of Bs and/or stars - as is typical GCSEs at this school. I would expect mostly Bs (or less?) if she had gone to the local state school. (Well, they will be numbers with the new system, but you know what I mean). So in my DD's case I think academics will be clearly better - because of better enjoyment, more effort (going with the flow of keen peers + higher expectations) and higher quality teaching. This I feel is worrh paying for. If we had a great state option it would be more finely balanced.