I think I found a spot to park at the end of the trail. It will most likely be the Metro station at Greenbelt MD. They have a long term parking area that costs $4.50/day. Parking is free at Metro stations on weekends and holidays. The ride ends on Memorial Day which means that I might get away with a week of free parking. Or I will have to pay $45. Either way, its better than the $140 I would have to spend at Reagan Airport.