"We like to do what turns us on artistically,” Delaney Martin, artistic director of New Orleans Airlift, declares of the nonprofit artists’ collective.

Dreamed up amid post-Katrina destruction and delusion, Airlift was formed with the mission “to collaborate to inspire wonder, connect communities and foster opportunities through arts.” To date, the Ninth Ward–based group’s signature project has been the Music Box Roving Village, an avant-garde musical archit...