Have you asked your DC for input? At the HS level, some may say the DC ought to be visiting/shadowing/sampling options and making a decision which the parents support, thereby fostering the child's internal locus of control and sense of responsibility for one's own education.

There may be something fundamentally flawed in leading with a DC's GAI? In theory GAI is calculated when there is a potential learning disability indicated by the IQ test, therefore this may cause attention to focus on exploring any potential LD as a concern for "fit" with any particular school option or learning environment.

In regard to #2, there have been several threads regarding homeschool and college admittance.

In regard to #3, I agree with Sweetie.

Has DC articulated what he is especially fond of at MIT, Cambridge, Princeton? Has DC frequented their websites and gathered information to help guide his decisions... as to how to get there from here?

Best wishes to your DC and family in choosing a high school.