Whenever a rock ’n’ roll figure moves to New Orleans—from biggies like Courtney Love and Trent Reznor to cult heroes Alex Chilton, Dave Pirner and Peter Holsapple—they’re usually absorbed into the city and recognized as de facto New Orleans artists. Indie-rock pioneer and Throwing Muses front-woman Kristin Hersh has been the rare exception. Her band’s 1985 debut remains an alt-rock touchstone and recent years have brought more notable work—solo albums, band albums (with the punkier Fifty Foot...