Okay this is pretty cool. After a great deal of research and study and attempting to understand the ancient languages she is singing in, crossed and compared with modern variants, Stef Conner has composed a number of tracks, remaking ancient Babylonian poetry into song.
So it is very possible that this is something like what it would have sounded like (minus the recording studio, though the did have batteries, so who knows?).
I can't get it to embed, so just follow this link.