I think you need a contingency plan Nan so something along the lines of if refuses to eat what you give her, she gets something else which is higher in calories, if this is refused could you offer her the supplement drinks?
If that doesn't work you plate up the food, budle her into the car and drive to a&e.
The hope is she will start to eat on the way there but if not follow through and get a&e to fully assess her.
Ultimately if you can't get her to eat at home she needs to be in hospital (regardless of what they've said.)
You have to show the ED you are on complete control and are not messing about.
The self harm and head banging is awful, I found that very distressing and difficult to deal with but again you have to do what you can to keep her safe so physically restrain her if necessary.
Tbh as with everything parent related it's always easier to advise other parents!! I certainly have not always got it right, I let dd drop two snacks a day fgs 🤦♀️ but I did have a bare minimum I would accept iykwim and would absolutely follow through if she didn't eat that.
I was also able to compensate for the snacks by ramping up the calories in everything else she ate.
You have to dig deep and be fierce against the ED monster, once it realises you will not back down life does get a bit easier.
I know sounds crazy but your dd wants you to force her to eat, she is bloody hungry!! The bastard ED will throw everything and more at you but if you stand strong it will eventually get tired.