In other words, if there's one thing I've learned so far in life, it's not to underestimate the power of simple human contact. Go knock on a random professor's door, and I think you'd be surprised how many times the door opens!
Really? I went to three different summer programs at Ohio State University when I was in high school. Great fun.
My last summer program ran nine or ten weeks and had me playing RA in a biochemistry lab. One of the most generous masters' students in the whole world (I think the poor guy was in his 3rd or 4th year... he was kind of a long-term masters student ;) spent most of the summer teaching me stuff -- growing bacteria, lysing them, running chromatography columns, gels, enzyme activity assays, the works.
He was crazy, actually, to spend that much time teaching a high school junior who would never come back to the lab, but I hope he's having a happy career somewhere because he sure was generous.
Obviously, if an organized program exists, take it! My point was that the absence of such a program does not preclude you from taking an individual initiative to do something creative.
Even if you don't care about the competition, it's an easy pretense for getting in touch and working with a professor. Plus, you might be able to convince your school to give you time during the day to work on your research (when I was in HS, we got a period every other day).