(As an aside: as an advisor of PhD students in computer science, I sometimes have to train students out of these habits. Research doesn’t happen if you’re used to getting the shallow answer more quickly, or if you’re afraid to be wrong.)
You seem to be coming from the perspective that testing must be the best metric, and then trying to develop a methodology based on that assumption. Purely as a thought exercise: it might be helpful to start from the assumption that testing isn’t an option, and think about what you might do instead.
Any student that can do any sort of undergrad level math like AP Calculus is going to find SAT math trivial in comparison. There's no way you can pass exams in the first but do poorly on SAT math, since all the stuff SAT math is testing on are prereqs for something like calculus.
At that time, the SAT was good at predicting the likely performance of a prospective college student … for one term. That’s it. I got an excellent score on my SAT (not a perfect score, but I thought that it was a bullshit measure — which, like all standardized testing, it is — so I didn’t care). I did well in my first term, and then not so well after that (I ended up doing fine in the end, but it took longer to get through a degree program because I didn’t know what I wanted to be when I grew up; I think that Americans, by and large, put too much focus on going to university too early and we would be better served by an extra year of high school and/or a gap year).
One other thing I remember from that time period is that a better predictor of overall success in school was NOBITH, the Number Of Bathrooms In The House. That is, socioeconomic indicators were a better predictor than anything else, including nonsense standardized tests like the SAT. And given that socioeconomic indicators are a better indicator, that is a strong indication that there’s seriously wasted potential at all levels of eduction because we mistakenly equate family socioeconomics with success in general.