Every night when things are steamrolling for Nathan & the Zydeco Cha Chas, the group’s accordionist and vocalist Nathan Williams will gaze into his audience, smile, and say, “I’m like a quarter horse. You got to walk me to stop me.” It’s a sign that things are going well, and the Zydeco Cha Chas are feeling their oats. The onstage groove isn’t about to fade away anytime soon.

In many ways, Williams is the living emb...