Nearly two years ago, a YouTube video went New Orleans-viral. Against a percolating sousaphone groove, five horn players—two trumpets, two saxophones and a trombonist—form a line under an impossibly low drop ceiling. Dancers crowd a tiny space in front of the band. There is no stage.

The players look vaguely familiar; the melody of the song is instantly recognizable. But everything else about the scene, from the clothes on the dancers and their moves to the...