Not keen on Dorothy - it feels dated to me, unlike the more classic Josephine (Dorothea or Theodora is marginally better but I still don't love it). Genevieve is lovely and would be my choice but is a tiny bit "soundalike" to Josephine.
Other suggestions to match Josephine (long classic names that have several shortenings):
Adaline (Ada, Addie, Allie)
Caroline (Carrie, Callie, Caro)
Charlotte (Charlie, Lottie, Callie)
Cecilia (Cece, Cissy, Lia)
Beatrice (Bea, Tris, Trixie)
Madeleine (Maddie, Lainey, Della)
Helena or Eleanor (Nell, Leni, Ellie, Ella)
Elizabeth (there's dozens! but I'd be tempted by Beth for the Little Women pairing)
Louisa (Lola, Lulu, Lou)
Catherine (Kitty, Kate, Cathy, Trina)
Georgina (Gigi, Gia, Georgie, Ginny)
Harriet (Harry, Etta, Hattie, Hetty)
Alexandra (Lexi, Sasha, Xandra, Alex)