> since the environmental factors that the poor tend to be more exposed to that lead to downward deviations from genetic potential have had significant impact before schooling starts (in many cases even in utero),

It's true that adverse environmental conditions can lower IQ, but not whole standards of deviation. There are many people who grew up dirt poor and yet managed to achieve academically, which if intelligence was really irreparably impaired by a poor environment would not be possible.

> and school performance numbers today basically just reflect the student body (and in very large part the engagement and socioeconomic background of the parents) they are dealt more than outcome differences produced by the school

Which is exactly why a genetic test would be more accurate! It would not take into account differences due to quality of schooling.