Millie can stand on its own. It sounds formal enough. I don't like it very much, though.
And out of those choices, I like
Mildred the most,
Milada makes me think m'lady and
Milana makes me think place. But my favorite name that can use
Millie as a nn is
Emilia (it's one of my faves. I was looking for an nn that wasn't
Emmy and got
Millie - but I didn't want
Millie.)