There is no adjustment whatsoever possible that will accurately further qualify/disqualify students from a gifted program, that is correct.

Simply "tightening" the existing fuzzy criteria will only further arbitrarily limit qualified students.

That's exactly my point. There's a system today that has some amount of arbitrariness to it. Tweaking that system slightly is almost surely arbitrariness-preserving, likely not increasing or decreasing it significantly.

My point is that it's increasing the arbitrariness by further constricting the qualified students pool.

Instead, accept they're all qualified insofar as they would maximally benefit from advanced lessons, and favor students for whom this may be their only opportunity to get ahead.