The fact that this sort of thing is done by so many organizations seems evidence that it's a good way to reach young people.

Hmm... I was thinking that no other organization does this, but I imagine that we mean different things by "this" – I suppose you are referring to the large number of organizations that sponsor a scholarship, as opposed to the lack of organizations that sponsor a scholarship with the specific goal of collecting information on high school students.

It might be wise to emphasize getting young folks to think about existential risks through an essay contest over gathering data about them.

Good point. The way this is publicized would be important – it might be worthwhile to consult professionals.

Here's what I found:

http://lesswrong.com/lw/82g/on_the_openness_personality_trait_rationality/

http://lesswrong.com/lw/9m6/the_personality_of_greatcreative_scientists_open/

Thanks! These are the posts I was thinking of. I've added them to the grandparent. One more tangentially related post (also by Gwern):
http://lesswrong.com/r/discussion/lw/ac4/online_education_and_conscientiousness/

I suspect this sort of competition is better run through FHI, if only due to their Oxford affiliation.

That's a good idea. The main obstacle I see is that FHI might not want to get involved in such an endeavor, especially since they are targeting only postdocs for their research positions, and have no programs for students.