Stanford of course is not in the Ivy League. It is however in the Atlantic Coast Conference, which might be even stranger.
You do not need a long list of ECs. This is definitely NOT a case where a longer list is better. Instead a short list of things that you wanted to do and that you did well is much better. Depending upon what you did, an internship with a professor could be important. Depending upon what the AI club did, being AI club president can be a very good EC. You might want to make sure that you listen to good ideas from other members of the club. “Leadership” does not mean getting your way. Listening to others and making the activity better is the point. I will confess that I do not know what USACO is (presumably university admissions staff will know). Regardless, admissions to Stanford is hard to predict.
Math plus CS is pretty close to what I did, and is IMHO a very good combination.
Some schools (MIT, Stanford, and Harvard come to mind) do not admit by major. Whether you get in will not depend upon your major. Some other schools (UCB being an obvious example, I think that UW might be another, or perhaps three other examples) do consider your major, and CS is typically a relatively difficult one for admissions. However, your stats are excellent, at least in my opinion your ECs are very good, and there are a lot of universities that are very good for both math and CS.