@myrtleWilson thank you so much for your comments, it means a lot to me anyone has replied, I've read a lot of this thread and I think the thing we all have in common is feeling a bit desperate, alone and wondering what the hell to do!
I think you are right, my dd is used to working as well, earning her own money, staying with friends, her own independence and if she had her choice, she says she would not go to the hospital or CAHMS (CAHMS have been very slow, one assessment in 5 months) ever, but she's quite compliant if I take her and we do this together. She just removes herself, withdraws or escapes (leaves house, hospital) if presented with food/eating she doesn't like, she doesn't speak or get cross or anything, just complete withdrawal and refusal which is why if she went into hospital (which she is threatened with weekly but manages to maintain enough to avoid it cleverly), she would have to be tube fed and likely leave and purge endlessly which is what she does when overwhelmed.
She also has pre-existing psychiatric diagnoses and trauma which pre-date (but undoubtedly have contributed to) the ED, so these things are always complicated. Keeping her indoors, in bed, away from friends/family or college is how she lived for two years of severe depression/overdoses, so I'm not sure putting her back there again is the right choice.
I think you are right about positive motivations- I do not go out with her unless she's eaten acceptably (protein, carbs) as I don't want her fainting, and motivating her with trips with friends, and family days out works very well. I like your idea of the longer-term motivations as well.
Reading these stories makes me feel less alone but also overwhelmed by how hard it is on the parents, I have been on the receiving end of CAHMS disapproval (amazing how they managed to make me feel shit in such a short amount of contact!) I cannot take more time off work as I'm already on informal pathway of performance management and it will be made formal with any further time out.
Thanks again for making me feel less alone, and I've really appreciated your insights (esp about therapeutic exercise which I think would be another avenue for my daughter as she is very motivated by being strong/muscle definition, but also see the dangers, she is currently on a gym ban due to lying/escaping my clutches!)