So sorry you are going through this, it must be a nightmare.
I think we are all moving away from your original question now, which is understandable, so I will try and answer your questions.
Last year we moved my DS from the local private day school to a boarding school an hour away. For a number of reasons but primarily because he was not happy.
We were open and honest with the registrar, he sat the entrance exam and was then interviewed by the Head. As were we.
I am sure if you explain why you are doing this the school will be as helpful as they can be. At the end of the day they will be interested in her school work and what she is like as an individual.
You say she is, deep down, a good kid (sorry un Mumsnet use of word) who is sporty and musical so the school will want her. If they have a place.
Call a few schools and see what the registrars have to say.
They will be able to answer your questions about taking her mid-year. If you are going to pay the fees I am sure they will take her tomorrow.
And the fact she is compliant is great.
My DS is thriving at his new school and a changed child.
Whilst it is a boarding school they are not locked in and could, if they wanted, walk to the end of the drive, hitch a lift, flag a taxi and be off.
And given that we give him pocket money he has the freedom to do that. It is not allowed but in theory he could do it if he wanted to.
You will need to be sure your DD is not going to do that.
What about Gordonstoun? That is in the middle of blardy nowhere isnt it?
Good luck with it. This must be a nightmare and it sounds like you are at the end of your tether.
Shame this guy can't just be locked up. I dont understand why he is on the SOR and permitted contact with your DD.