I am certainly no expert, and there are probably many others who will advise you better.
My opinion is that you should focus on what would distingusish you, which in your case is A LOT. I mean write about your IMO medal (again congrats!), your IMC distinctions, your tutoring experience, your departmental awards and some weight to your publication. Explain briefly what you would probably like to work on and why (for example continue some work performed in your publication since you have already performed original work-which I think is the most important qualification). The best SoP in my opinion I have come across in the Internet is http://ms-phd.com/Archive/2006_03_09_st ... chive.html
and it seems to me that you have the same qualifications as that guy. Again, I warn that this is clearly a personal view. I am applying this year as well but aside from writting my own SoP based on what each university says they want, I have no other experience.
My SoP will be much more moderate than yours. Since I am interested in algebra, I wrote about the most advanced algebraic topics I have covered so far, and some unofficial lectures I gave in some courses and explained how the latter motivated me to choose my intended field. Your experiences would have much more weight I believe, since you have them published officially.
Since I see that you are an international student as myself, my most important advice is to go and give your transcripts for official translation ASAP if you have not already done so. I'm still waiting for mine (the ministry in my country translated manifolds as .... multiplicities
so I had to go to another translator). Also have in mind that GRE/TOEFL scores take some time to be sent so have them sent ASAP as well.
Finally, it may sound a bit naive, but if I had your qualifications and a vague idea of my intended field of study (eg analysis) I would just select the top 10-12 universities in that field and apply just to them (ok possibly 1-2 in the 10-20 rank too but not lower than that). If a person with your qualifications does not stand a chance for Harvard, Princeton, MIT, Stanford, Berkeley, Columbia, Chicago, UCLA then who does?
In any case good luck!