Given the number of transitions within the public option, the lack of improved curriculum, and the likely lower standard of customer responsiveness in the public system, you're deciding on the basis of cost and potential peers. Only you and your son can gauge the weight of these factors. I think you should make a balanced scorecard and weight these (and other) factors to inform your decision.
It's probably unorthodox from the public school's point of view, but would the GT school let your son visit for a day to gauge fit?
I will provide this comment from personal experience. Small, private schools are flexible and accountable in ways that public administrations with bloated bureaucracies are not. I have been dissatisfied with the lack of advanced curriculum provision by DS' small private school, but its flexibility has meant that I can impose my will where needed to achieve what DS needs in areas where the school's offering is lacking. Were I to enact similar advocacy in a public setting, I would be outright stonewalled or facing an administrative lead time of upwards of 20 months, and it would still achieve mediocre results.
For us, I've prioritized customer-centricity and flexibility, because DS' needs change and accelerate with sufficient frequency that the public advocacy cycle can't keep up without demoralizing DS.
