Many thanks to everybody for taking the time to assist me with this dilemma. ^

I think that I'll try to find out whether NH would be able to check my bags through to LHR on a separate BA ticket. I remember (now that I've been reminded) that I need to collect my bags and clear US Customs but there is usually a recheck desk just beyond the Customs exit.

Should I be unable to recheck the bags I think that the rental car may be a great idea. I have taken a look at Alamo and have found a basic car for a little over $50. I can then dump the bags into it and then either leave it at Udvar-Hazy (knowing my luck I'd probably just miss the bus and have to wait another 40 mins for the next) or in one of the airport car parks before catching the coach to West Falls Church and then jumping on the metrorail to do a quick spot of sightseeing.