Many thoughtful comments above.
I think that when we are considering learners in a very small percentage of the population, there will not be a single approach that is indisputably the "best" for every one of them. The diversity within this 5-6% (a relatively generous estimate of the GT percentage) can easily be as great as that within the middle 68%, if not greater. I would agree that critical considerations in schooling focus on academic and social-emotional development. But the foci of need and appropriate structures for supporting growth in primary need areas vary from child to child, and from moment to moment for each child.
We have taken a flexible approach to school placement that is open to new approaches during and between school years. None of our children have been in congregated/substantially-separate gifted programming, but they have experienced significant modifications, including homeschooling, in-class differentiation, subject/grade acceleration (including dual enrollment) and early entry, many of which were available because of careful school selection, based less on the nominal structure of the school than on how amenable administrators and teachers were to working with our children's specific needs and strengths.
Our criteria have always been: are our children happy, learning, growing, loving and feeling loved? If yes to all of the preceding, then this setting is working. If not, then we problem-solve and work collaboratively to improve the setting until it becomes clear that it is intractable. Then move on, even if it's the middle of the term.
We also have not placed all of our dependence on school for these important areas of development. No matter how fabulous the school fit is for a child, we are still the parents, with many other venues outside formal education for nurturing their holistic growth. Just as no one person can meet all of the needs of any other person, no one school can meet all of the needs of a child. Use your community of caring adults and children, of diverse abilities and interests. One may find one's "people" in or out of school, and, more importantly, if open to it, one may discover that there are multiple dimensions on which connections and affinities may be discovered.