I would strongly recommend visiting GDS and asking current families in grades 3 and 4. There's nothing you said about your son that sounds unusual for a third-grade boy — I'd almost be more worried about a nine-year-old who DOESN'T crack up at a good fart joke, or even a bad one. The way he'll become an adult of good character is by being surrounded by adults of good character, not by trying to be an adult as quickly as possible.
I know GDS very well, and there is no reason GDS wouldn't serve a boy like yours well. The bigger question is whether their approach to education resonates with yours. There are many schools out there; investigating a few of them may help you narrow your search to the kind of school you're seeking. If you live near GDS, and you're looking for schools with similar profiles among accepted students, you might look at St. Albans (a single-sex school), Sidwell Friends (some people find it less individualistic than GDS), and Sheridan (a K–8, where the ultimate focus is on childhood instead of teenage-hood). There are many, many other excellent options (some of which don't begin with the letter "S," haha.)
Meanwhile, let the little rascal be the age he is, and don't worry about whether his behavior is "good" or "bad," desirable or undesirable. Be attentive instead to whether his behavior is NORMAL. I recommend two resources if you haven't investigated them yet:
1) "Knowing Third Graders," a part of the Responsive Classroom series. The pamphlet focuses on what third graders are like. It's geared toward teachers, but entirely accessible to parents as well. Best of all, it's online, and free!
https://www.responsiveclassroom.org/sites/default/files/ET3intro.pdf
2) Richard Weissbourd's excellent book, The Parents We Mean to Be, a smart and thought-provoking introduction to the moral development of children, the roles parents play, and the damage we can do to our children by insisting that they need to be "happy" all the time.
Good luck!
Peter
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Disclaimer: The anonymity here makes me uncomfortable; it's too easy to write uninformed, personal, or mean-spirited posts if people don't identify themselves. For that reason, I have an account so you know whose words you're reading. I have more than 20 years' experience as a teacher and administrator in independent schools. I have read hundreds of admission files, and I have counseled hundreds of students in finding their next schools in the DC area. If you don't like something I've said, you're in good company — there's a long line of past students and parents ahead of you.

If you want to chat further, please feel free to contact me offline: peter <at> peterbraverman <dotcom>