My 25 cents worth: DCA is a primary airport in a full time Class B Surface Area. Thus, the airport is not a full or part-time uncontrolled airport. If it were me I would feel uncomfortable that I was unable to contact the tower. And, I have no doubt approach control would have been unable to shed any light on the matter.
So, and this is strictly the way I operated, I would invoke the principle of "the least cost of being wrong." I wouldn't be able to process what may or may not be wrong at this highly sensitive airport. Also, what assurance do I have that the runway is clear? If this were an authorized uncontrolled airport in my ops specs the company may very well have a responsibility for checking the runway for night operations. Not so at DCA.
That's enough of a confusion factor for me; I would have diverted to IAD.
I am not arguing the legalities because sitting here at the comfort of my desk I don't know what violations, if any, I would cause by landing at DCA under the circumstances. I do know that diverting to IAD would not create either a legal or possible safety issue.