When I read "Evelyn," I pronounce it EHH-vuh-lenn. Based on that, I don't like the flow of Adelaide Evelyn, although I like both names individually a great deal. Adelaide EEV-lin does flow better, but at least in my corner of the world that would not be the intuitive pronunciation of her middle name. (Perhaps it is where you are from!).
Other ideas: Eve, Elise, Eliana, Evangline, Elaine, Eloise, Elora, Eliza