We landed our airliners at night at the old B52 base at the west end of Puerto Rico every night with no controller. We usually cancelled our IFR clearance before switching to advisory frequency to simplify things and not have to cancel after landing. Pretty simple procedure but uncommon for our airline. DCA would make it more difficult because it should be controlled but isn't. I think I would go around and sort it out with approach control like the first arrival did. If approach says treat it like an uncontrolled airport then it is easy. ATC is for traffic separation, they have little control of how you conduct your approach or taxi as long as you are not going to hit another moving vehicle. They should have just closed the tower at 11:00 and made it uncontrolled to make things simple and he could sleep in his own bed. Sleeping sitting up sux.