Which online AP courses should I take this summer to better my chances at admissions?

[skieurope]

If you were talking to someone with 93+ averages throughout freshman to junior year, had taken no AP courses, but was being barred from taking >2 APs next year for whatever reason, would you say online courses might help?

A huge emphatic no.

I will take the liberty of quoting @skieurope 's oft-quoted statement from AO’s at Columbia, et al: “Please don’t do that, it doesn’t impress us.”

Quite right. And this is not me saying this; this is AO’s telling me this.

Colleges expect students to challenge themselves within the curriculum available at their HS. You attend a very selective HS with which every AO in the country is familiar, so it’s not like you cannot be challenged there. (BTW, I deleted your link to your school profile - this website is called College Confidential for a reason.) You would be better off politely asking the school to reconsider the 2 course cap in your case based upon recent performance, since it’s not that the school limits all students to only 2 AP’s; it limits students with your cum GPA to only two.

But I think it might be feasible that I can get in 1 or 2 tiers lower, e.g. Columbia or Cornell

I’ll take your word on the feasibility, but will disagree with you that these schools are any lower tier.

Congrats on dealing with your anxiety issues. Best of luck.