I like this future for Éowyn quite a lot - and the allusion to Florence Nightingale is a clever and very suitable one. It's so easy to see her superficially as some model of caring and nurturing Victorian womanhood and thus completely misrepresent her amazing achievements. Similarly, the White Lady of Ithilien would have had her work cut out for her, with or without a sword. (And healing is so much harder than killing, in the end.)