SweetChestnut. I'm in EXACTLY the same boat, though we're three years ahead of you.
My DD was ill of and on through Year 8, and was generally diagnosed as having tonsillitis, was prescribed antibiotics and soldiered on. If only we'd known that the antibiotics were not really having any effect ( and indeed were adding to her malaise), she "recovered" by herself from what was clearly viral ( despite the white spots on the back of her throat) and what she really needed was a lengthy period of time off school to recover.
We went to see Dr Crawley too who was lovely, but DD found the pacing a little unrealistic. She insisted that she couldn't miss lots of school and instead we came up with an arrangement which meant she missed "non essential" lessons, which was do-able because we live very close to school. Just meant she missed the "fun" lessons and I wish I'd had the sense to do what you and your DD have done and insist that DD took a big break from school. I'm at fault too because I was concerned that year 9 was very important and to miss much of it would impact on her GCSEs but I'm sure that wouldn't have been the case.
Anyway she has soldiered on, with periods of coping, a rush of adrenalin when exams approach and then a crash after them. Esther Crawley would not be impressed. She now sees a sympathetic GP every couple of weeks who has prescribed her with amytryptline as well. Her dose is now up to 75mg and seems to help her muscle pain and sleep difficulties a bit, but she has put on weight which may be a side effect, or may be a result of no exercise and eating of comfort foods to get her through exams etc. Probably a mix of both but enough to make her determined to cut it down and out after current academic year.
DD is now in year 12, so one week into AS exams. She got her GCSEs and did very well. School made her drop from 10 to 9 subjects ( slightly to her and my annoyance because it was clearly driven by her latin teacher not liking having to mark work out of time rather than concern for her. Dr Crawley had suggested that we agreed with school that homework could be done over the weekend rather than on week days which helped DD but wasn't fully embraced by many of the teachers, particularly the Latin one). (She ended up doing 10 though because being in set one for Maths the girls did Additional Maths). She managed OK. A few friends rallied round to copy notes if she missed lessons but she managed to attend most lessons for the GCSE subjects. She worked through the holidays to catch up as well. And ended up with 10 very good grades.
AS year has been a bit easier. I think as she's got older she is able to control things a bit better. It helps only doing 4 subjects for AS, which are her favourite subjects, with study lessons built into the timetable, which mean she is home at lunchtime on wednesday and Friday and sometimes comes home for 2 hours on a Tuesday. It does mean, though, that she continues to miss the "fun " extra curricular things which take place in the lunch hours, and it does mean that she missed out on being nominated to be a prefect/house official earlier this term. A teacher said to me at a school event when I mentioned DD's "oh but [DD] isn't often in school and doesn't go to many clubs" and clearly knew nothing about her illness. All that sort of thing still upsets DD.
She does get depressed about it all, I know, though fiercely argues that any of it is in her mind. I do try to explain that while the CFS is clearly a physical illness, part of its effects will quite understandably make her depressed. She's down to see someone for CBD at Kings, but that's quite a way for us and we've had to cancel several appointments - the thought of driving and hour each way and having to go over all her symptoms and concerns is just too exhausting for DD to contemplate most of the time.
I am wondering about giving the Lightning Project a try, but for now DD is just trying to get through her AS exams.
Sorry, a huge ramble there, and not much advice to you, but I'd love to use this thread as a way of sharing experiences/getting support.