I see this issue, from the administrators' perspective, as being the intersection of two concerns: resourcing and needs identification.
On the first front, at the risk of sounding simplistic, with a theoretical population of ~5k students, NYC has a scalable opportunity to provide HG+ programming at cost parity to general ed programming. To my thinking, this is just a matter of districts doing their operations due diligence before implementing a reallocation of general resources to gifted ones. Note I didn't say "expansion" of gifted resourcing, as that connotes more total resources being required, which isn't the case.
Regarding separating the truly HG+ from those who only appear to be, incentive compatibility could be achieved by actually implementing HG+ curricula. Make the course content so challenging that failure is all but inevitable for those students not targeted by the program. After a few years, parents pushing for non-HG+ gifted enrolment would have the reasonable expectation that their children would be failed. You might never get the non-HG+ contingent down to zero, but you could be successful directionally.
