When I travelled to Florida, I did not bring my firearm for many reasons. One of those reasons was I was taking the subway from my home to the airport in Virginia, but would pass through the District of Columbia.
I may have been protected by the FOPA of 1986 (firearm owner protection act). Specifically the Safe Passage Provision. As long as it looks like I am going THROUGH DC with a case locked gun I am fine, as far as the Fed law is concerned, no matter WHAT DC laws are. DC get's legally trumped.
Still... It might make legal cover, but I'd hate to try to explain the finer points of the law to a DC cop. My assumption would be that despite being completely in the right, any interaction with law enforcement involving a firearm locked away in my luggage would amount to a huge hassle in the best case scenario.