If she is on the 12th centile, she isn’t that thin yet.
Is she really not getting 500 calories with the ‘fat’ balls that she is willing to eat, plus nuts and veg? 500 (kilo)calories is a very small amount.
I went to a talk on this with one of the private units that treats anorexia and they said the first stage of treatment was basically entirely focused on making them eat. Apparently, until they get to a basic weight, they are not that amenable to psychological treatment, as their hormones and mental processes have also become unbalanced.
So, until she can be seen professionally, I think the focus should be food, using whatever levers you can to make her eat (whether it is bribery, blackmail, or just not letting her leave the table until she has eaten a basic amount).
If the NHS eating disorder unit cannot see her, there are private facilities that specialise in this (obviously they aren’t cheap). If you have the resources, I would look into this.
It is a horrible condition and you have my symp