Waves of roots rock and soulful introspection come crashing one after the other in “Swept Away,” the transfixing new musical that officially opened Wednesday night at Arena Stage. Inspired by the Avett Brothers’ 2004 album “Mignonette,” about four men stranded in the Atlantic Ocean after a 19th-century shipwreck, this morality tale launches with toe-tapping propulsion before anchoring for an intimate elegy on grief and guilt.