So how does a genuine polymath who is-- well, a real kid-- demonstrate that they are polymaths with wide (but genuine) interests, and not just a dilettante looking to rack up a bonus score?
...
How do admissions committees tease apart which is which there?
I'd think it works just like resume's. There aren't special formula when it gets to the readers. I'd guess they are following gut instinct and figuring out why some stands out. Ideally it tells a story about who the person is... a bit of art on both sides.
If you think of your daughter's story, opening with a scene of a 14 old college application you're already fairly deep into an interesting story. If I were looking at her application, I'd assume she learns quickly with a good chance she plays an instrument well. The next chapter is where is her passion, what is her character like, and where is she going. A consistent long term activity with a single non-profit, a summer internship in a science field (with great refs), and her current level of proficiency in marksmanship (title IX opps and interesting.) That's a pretty good story, why overwrite it?
