At one point, I thought I heard that they were going to put some charging connections at the TyCo Service Center where you could grab a charge, if needed. If Tesla installed a few chargers at the service center and they were available 24/7, that wouldn't be a bad alternative, as TyCo isn't too far from Dulles.
You could go to the Tysons showroom and get a charge (less than a mile from Tyco), but it's also hit or miss.
There's usually a bunch of Tesla's parked there (the handful of times I've been), and the only parking spaces I've gotten were next to the NEMA 14-50's (I think they have HPWC also).