Camille nn Millie gets my vote! I think Camille is classic and sounds very sophisticated and beautiful, and Millie is sweet and adorable. It's a name that would work for a child and an adult. Love it! And it goes so well with your other girls' names.
Thanks for the Mimi suggestion! Our other nicknames are already ones that people don't necessarily guess when they hear the full name, so we think it will work for us. Now just to find a middle name we like with Camille.