There aren't many middle schools in DC that don't go to 12th. St. Patrick's, Sheridan and Lowell are the only ones I can think of, with Sheridan being the closest. If you're willing to consider Bethesda, there's Washington Episcopal School (WES), on River and Little Falls Pkwy, which isn't much more than 10 minute drive and Norwood, which has a bus service from Chevy Chase, DC.