The other location is a Children's Hospital that a friend of mine recommended. It's where she took her two sons and they were diagnosed with dyslexia. It's a little more expensive though and I'm not certain of their experience with gifted or 2e students.
I don't think my dd is gifted, but she's definitely above average in her thinking, problem solving, and perception of things in everyday life.
Given the scores, and your description that your daughter is 'above average' I think it's time to stop worrying that she'll be 'too gifted' to be understood by the Children's Hospital. I think they are by far the better choice, and if they are more expensive, at least you have a chance of learning something that might help you - while getting another IQ score just doesn't seem likely to generate a way forward for you from where I'm sitting.
Love and More Love,
Grinity