The leader of New Orleans’ DIY hip-hop movement lives half an hour outside city limits. Gabriel Major (a.k.a. Delish Da Goddess) resides in the sleepy town of Violet, an unlikely origin for a rap deity. “Being from Violet, everybody is in that bubble, so it’s easy to feel comfortable there,” Delish says. “There’s so many musicians in Violet that’s afraid to leave Violet. And me being a rap artist, there’s not a venue in Violet that would allow me to play there. There’s no open doors.”

Stil...