Rather than attempt my own answer to this complicated question, I'll add some explicit links and literature references to help the discussion along. The classical Demazure character formula and its generalization to symmetrizable Kac-Moody Lie algebras have a long and difficult history, starting with Demazure's own influential but somewhat flawed paper. It would be helpful to get feedback from some of the still-active participants, of course, including Joseph, Littelmann, Andersen, Kashiwara. Meanwhile, here are some details about the papers mentioned (though the one by Kashiwara probably needs special permission to access online):

Joseph, part I here

Joseph, part II here

Kashiwara: The crystal base and Littelmann’s refined Demazure character formula. Duke Math. J. 71 (1993), no. 3, 839–858.