Like too many students, you have a misplaced faith in APs as your ticket to selective colleges. As long as your GC will tick the box saying that you have taken a "most rigorous’ course, selective colleges don’t really care about APs per se. In schools where APs are offered, 5-7 is fine- and there is a point where it can start to look less good, rather than better to have a ton of them- especially if getting so many done is at the expense of ECs.
In many schools, the top tier of students take all APs in Junior/Senior year, but the main benefit is that it helps their weighted GPA, and can make a difference in class rank-and that is true ONLY for the APs they do through school. Self-studied ones only help for getting credits for college, which most selective schools limit, and for applying to international universities. Remember that you have 2 GPAs- weighted & unweighted, and selective schools tend to look at the unweighted more- not least, b/c as you have noted about your school, the weighting systems at different schools are so different that you can’t meaningfully compare them.
And: your stats (GPA, test scores) just get you to the ‘qualified’ level. The "admitted’ level involves those, plus LoRs/essays and strong ECs.
tl;dr: the only person who thinks that taking 6 APs + a Study Hall looks bad is you.