Following this thread as I have the same dilemma about when S23 should take the SAT. Lots of helpful info has already been shared.
My D took the SAT fall of junior year (before the PSAT/NMSQT) and had to review algebra concepts learned two years prior. S23 is in Algebra 2/3 now. My thought is to have him take it next August which will give him the summer to study and a score that can count for NM consideration.