Somehow I didn't think you were going to be willing to answer the where question very precisely at this point! Well, in the unlikely event that it looks as though it might be my university [I'm far enough away subjectwise that I wouldn't have heard] feel free to PM me if you'd like to discuss schools nearby. Yes, it's probably too much to hope to find a school that has experience with children as far ahead as your daughter. DS's school (a small independent school with small classes) is working out basically because they seem to be good at treating each child as an individual and being flexible in what they expect. He's currently with age peers, though with his maths run entirely by us. I don't know whether this will continue to work, but so far it seems fine. It's really down to excellent teachers who don't have fixed ideas about what Nyos can do.
We would be in a maths department, actually, so you might hear about it; the center would join a maths department with physics and astronomy. But not in Scotland: none of the Scottish universities (Edinburgh, Heriot Watt, St Andrews etc) currently has a strong enough theoretical physics profile to be attractive for us.
Yes, I had an OK school experience in a UK private school with this kind of attitude. We looked at some British schools where we currently live and were shocked at their obsession with testing and SAT levels. They wanted to use SATs as the only measure of DD. Once DD had demonstrated she could do KS2 papers, the next thing they did was give her KS3 papers, GCSE papers and so on... we just ran a mile. Her current school isn't perfect but is at least not obsessed with testing, is willing to work with us, and lets us take charge of her maths, propose enrichment activities etc.