I love Josephine too, and would put that at the top of my list: it's strong, elegant and classy. May is also a fab first name and goes well with your boys, although I would stick with the -y spelling.
Alice and Nina are nice but a bit too plain against your boys' names imo. Love Elsa (DH vetoed ) but not Elsie - I suppose whether or not it sounds like Ailsa might depend on your accent Also, not sure it works with Edward.
Don't like Florence or Philippa, not fussed about Alexa.