Not sure if she fits in with your description, but I think that Jennifer Warnes is very much under rated with a superb voice. Most will cite "Famous Blue Raincoat" as her definitive album. However, I personally think that "Shot Through the Heart" and "Hunter" are both superior albums in terms of content, if not sonics.
Try also try, Marlena Shaw "Live in Tokyo" on Eighty-Eights, a Japanese pressing, of you can find it. Maybe it is on CD, too, I don't know.
I like Eva Cassidy, as well. Also, Janis Ian "Between the Lines" and "Breaking Silence".
Have you tried Dinah Washington?
Try also try, Marlena Shaw "Live in Tokyo" on Eighty-Eights, a Japanese pressing, of you can find it. Maybe it is on CD, too, I don't know.
I like Eva Cassidy, as well. Also, Janis Ian "Between the Lines" and "Breaking Silence".
Have you tried Dinah Washington?