DC Eleven, DCYFC will be the best options based on what you described.
Everything is sane within these clubs, the travel is local and people have multiple kids doing multiple sports so carpooling and collaborating are easy within these communities.
You will have your choice of Arlington, Alexandria, Bethesda, etc. if your child wants to get more competitive later.
My best tip is since you have a rec team built around an elementary school, you best bet is to have them start playing pick-up after school together and just participate in small tournaments like
https://3v3live.com or
https://5v5soccer.com. McLean has one coming up. Small format is best for development and club soccer screws that up.
Get some Bownets and pennies and have them play organically every day after school. You can get create group and parents take turns and hire someone to watch them and possibly hire a coach once a week to do some ball mastery with the group. Carter Barron fields are wide open all of the time as an example. Do the False8 ball mastery volume 1 at home a few nights a week and you will skip ALL OF THE DRAMA but have a kid who would step onto ANY 1st team in the area by U11/U12 because he understand how to master the ball and he would have had pure fun with his friends for 3 years and WANT to push to the next level on his own.
This is the way...