When I was young and single and living in that area I would park at the Holiday Inn and hop on the shuttle to the airport. Once I got back I'd take the shuttle back to my waiting car. Free parking!!

Once I got married and my wife would give me that look if I suggested that option I figured out that it's still cheeper to book a room the night before or after the long trip. Priceline will usually find a hotel around Dulles for about $35-45 where as the blue/green lot would be $63-72 for you week long trip. So book a room the night before, have dinner at the Green Tree up in Leesburg, and get a good night sleep before your flight!