Wow! Your application will look outstanding! You see, the Ivies all have a system of some sort with point application. Any extra curricular and award has its own point award value on the system, and in your case, I'd say that you definitely have a high enough number of points to stand out. Of course, your rank and weighted GPA... Lol, speechless.
With that kind of application, you'll probably pass their first round of elimination. I had a friend who's in Stanford and had a similar application, similar problem. She just took the ACT and scored a 35, got in to her dream school.
As for SAT II, I'm not sure about the Ivies, but I do know there are a good bunch out there that don't look at the scores until you're a student. It's more commonly used as a way to gain credits.
Oh and by the way, from seeing my elite friends graduate, it looks like you might be best for Stanford (I know it's not Ivy, but still...) and Harvard. The other Ivies seem a bit more technical on having high SAT's, getting academic awards in math/science, etc. Stanford and Harvard are more focused on people who have great time management and pretty good class rank.
Princeton, however... I don't really know if it's the best. Same with Cornell. Meh. They're more geared on "book smart" (almost full score on SAT, national science/math awards, etc) Word of advice: be prepared for bloodshed if you get into Cornell (at least in the math/science department...)
By the way, all the people accepted tended to have VERY VERY VERY good college essays. Just a tip.
Happy applying (and thanks for chancing me)!