Gregory Davis distinctly remembers a comment made to him 25 years ago when the Dirty Dozen Brass Band was in its infancy. On hearing the unconventional take the ensemble applied to the brass band style, an older traditional jazz musician responded, “You’ll never make it to Carnegie Hall doin’ that!”

“I guess that stuck in my head,” says the Dozen’s trumpet player, who had the ideal opportunity to respond a decade later. “The night ...