Thank you, lots of good points here. I'll try and answer as many as possible!
We are fortunate that we can pay the fees if need be, so we don't need to wait for the tribunal process to conclude before she moves. As she's not in a phase transfer year and is technically in a school, I don't know if we will get any sort of priority on the waiting list but we can live with that.
The school has an excellent reputation for pastoral care through various different sources - here, Good Schools Guide, word of mouth. Some of the things they suggested they could do (unprompted) really put my mind at rest. My eldest also encountered a student there (entirely unrelated circs) who volunteered (again unprompted) that they had ADHD and had found the school really supportive. DD doesn't actually need a huge amount of support, she just needs her modest support needs to be taken seriously when they arise and this has been the issue at her previous schools - we flagged them but they weren't taken seriously, or only by some staff, or too late. She says she doesn't mind a large school environment (from a sensory perspective) but the fact is she just gets overlooked or dropped down the priority list as everyone is so busy and overstretched.
DD is keen to go back to a physical school and was on a real high when she left the assessment. She said it felt very different from her first big school. Some of her peers at her online school have really suffered with long-term burnout - fortunately she didn't get that far and is now in a pretty good place thanks to time away from her old school and a great therapist, who is on hand to help with the transition (both directly with DD and providing advice to the new school). She has had some school years in the past where she has really thrived in the right environment (good teacher relationships) so I really think we need to give this a go, although I know it won't be plain sailing.
I think they are suitably secure - they are part of a larger group and have expansion plans. I am a bit concerned about the longer school day but hope the shorter terms will partly offset it.