I would agree that you need to be looking at private schools but even there you could face difficulties. They will have the ability to be more flexible but they are also typically likely to be working at a higher level which will make catching up even more difficult. School fees will typically be circa £15-20k per annum.
Just to stress, nobody is doubting that your dd might be very intellectually capable. That isn't the issue. The issue is the sheer amount of content she would need to get through in order to take and perform well in the exams. She will have missed more than half of the work required to take the exams. These are 2 year courses. Lots of schools cover the work over three years, particularly in the core subjects and by the time your DD starts they will have almost finished. My DSs go to a selective independent school and they start the GCSE content in year 9. By the second term of Year 11 they are finished and are revising and extending.
IMO you need to find a school asap and find out which exam syllabus they are working to. You can't tell from the location of the school. I'd then start her on the curriculum already. In fact I'd even consider taking her out of her current school and getting private tuition whilst you're still in the US on the UK syllabus content.
My DN has done this the other way around and DSis found that although he was bright, the syllabus in the US was just so completely different to the UK that it took an enormous amount of work to get him up to speed.
She will probably be required to take around 10 subjects
maths
english language
english literature (find out the syllabus immediately and get her to read the books)
chemistry
biology
physics
history or geography (or both and only two sciences - history would I suspect be a tricky option here since the content is unlikely to be stuff she is familiar with)
a modern foreign language (french, german or spanish - presumably she's done spanish?)
something else - typically something like art, DT, drama (none of which she would have time to cover now due to the coursework content) or computing, food technology etc (which might be doable). At a private school latin is likely to be an option in this category. Latin GCSE is part language and part analysis of literature.
If it was my child I'd look at staying in the US for another year as the first option. You are moving her at the worst possible time for the UK system. If you have to move then I'd look at a private school and push for her only to take 8 GSCEs so that she can use the free periods supervised in the library to cover the content she's missed (not as likely to be possible in a state school where they are unlikely to have a FT librarian). I'd also be getting her a tutor (circa £30-£40 an hour)