Interesting post to read and a lot that I can relate to. DH and I are both academics in the sciences, so I know where you're coming from.
Just on face value the progression schools sounds very interesting (obviously factor in, personality etc. like PP said) but I wonder how good it is in practice? Is it possible to ask if they have had experience with gifted children in the past? Do you know any other parents of gifted children there? One small red flag I saw in your list was the group projects. Group projects tend to be bad for gifted kids and many times they end up carrying the vast weight of the project.
Another thing. If you picked one school or the other could you switch later on if it was a bad fit? I know about math tracking, it was something I had to deal with at the same age when I switched into a public school but at the time they let me test into. If the progressive school was a bad fit could your kids do the same?
FWIW, I agree to you to a certain extent about the 'elite' university. More in the sense that it makes your life easier later on (by using the name). I've seen first hand how sometimes a name can just get your foot in the door. On the other hand, many small privates (at least for college) offer better scholarships and have way more interaction with the teachers, so there's some positives there too.
But, in my experience, for grad school you really have to go for the biggest name possible...
