Billy Walsh didn’t have his own bedroom until he was 30 years old. Now he presides over his own private Eden. Walsh’s journey—from his hardscrabble youth in Boston’s Jamaica Plain neighborhood to his ascendancy as a top songwriter and music impresario—has all the makings of a modern-day Horatio Alger story. He spent years hustling as a dancer, nightclub promoter, celebrity stylist, and fashion des...