> There was a stark contrast between those of us who had designed our projects completely ourselves, and those who had significant mentors/lab affiliations.

Love to see someone confirming my cynicism. In high school, a science teacher asked me if I were interested in doing something for the (then) Intel Talend Search. I looked up the previous finalists / winners and noticed that an overwhelming majority of the kids were in cities with top tier research universities (or did math stuff, those kids' locations varied a bit more). At that point, my spider sense told me that it wasn't worth the effort to try to compete without the backing / mentoring of a credentialed adult.