No AMC testing here, but my kids mostly did the PSAT in 8th, 9th and 10th as a requirement at school. It varied due to Covid on who took which over the past few years. Then during the summer between 10th and 11th grade, they do some studying - mostly a few practice tests and then working on the problems they got wrong. My oldest did the July ACT, September and November SAT and the October PSAT. It was probably too much, but we both expected some to get canceled, since it was 2020. The next one just did two SAT and the PSAT during the same times. Both had had Algebra 2 in 9th grade and AP English Lang in 10th, so it seemed to be a good time. Plus, they had much more free time in the summer than they did during the school year. And it got them studying for the PSAT. My oldest is NMF and the next will be commended. They were both glad to not have to study for the school day SAT in April, as they were studying for IB and AP tests, busy with robotics and the musical, etc. Adding more would have been very hard on them.
My youngest just finished 9th grade, but was in precalculus, so we are considering having him take the SAT in August while the math is still fresh before AP Calc next year. I’ll still have him work next summer though for the PSAT, so we are on the fence for it this summer.
Maybe that gives you some situations to consider in your timing.