Any city would LOVE to have 20,000 young adults come and spend a few days. The tax revenue is enormous.
Tourist destinations make for cheaper flights and hotel rooms. Huzzah for capitalistic competition.
Security in DC is not THAT tight for most places, including the Smithsonian. At the Air&Space museum, friends had their Kershaws, but were only turned away because one of them had his Kukrari (almost a machete). No one will get arrested for having a screwdriver.
Whats this Senior Trip you speak of? Most of the school groups that take the tours and such of the museums are far younger, I did mine during elementary and middle school. Far to many places have standardized tests that are far more important then frivolous things like going to the Air and Space Museum.

(I don't like that new rolleyes)
DC is indeed crowded in April, for that is prime weather time. The Cherry Blossoms also tend to bloom around then, and that is the most crowed time of them all.
That said, there is no real good location here to host nationals. There are places to hold a regional, but nothing large enough to host the Championship. Unless you setup like Epcots parking lot, but on the Mall. The exposure there would be HUGE, as would the costs, but the PR would be enormous.
Wetzel