Denyce Graves as Carmen, Washington National Opera (photo by Karin Cooper) This year’s production of Bizet’s Carmen (see the piano-vocal score) was a late addition to the company’s 2008-2009 season, reportedly displacing another production to a future season when its star, Denyce Graves, became available. The American mezzo-soprano, born here in Washington and an alumna of the Duke Ellington School of the Arts, is a favorite with local audiences. For all of her struggles…