I'd send the extra letter, as it will probably help paint a more full picture of your son. I wouldn't send items more than about 2-3 years old, unless they're really spectacular, and none as far back as 7 years ago. Instead I'd provide a full narrative of his progression, early milestones, etc. in your written portion of the application. Get creative on ways to show what he can do and what he knows; for example, lots of parents submit videos of their children speaking in depth about areas of interest.
Regarding math, I'd provide samples of his current schoolwork. These will not count against him, as I understand it, especially since Davidson must be familiar with the problem of not getting enough acceleration. I think having do some more advanced work is a fine idea.
