Some lovely middle names for the beautiful link here - Astrid, Jolie or Teagan would be my picks. I also like Astrid and Teagan as first names and think they go well with James or Joseph.
If you like Annabelle but want to avoid the Belle bit how about:
Anastasia, Annalise, Anaïs or Anamaria
Otherwise, I think James and Joseph go best with other solidly classic names (I don't know if any of these have Greek origins):
Abigail, Amy, Beatrice, Charlotte, Emma, Emily, Eleanor, Evelyn, Florence, Felicity, Grace, Georgina, Harriet, Hannah, Isabel, Imogen, Jessica, Katherine, Katie, Lucy, Laura, Melissa, Matilda, Madeleine, Natasha, Natalie, Olivia, Philippa, Rebecca, Rosie, Sophie, Sarah, Scarlett, Thea, Victoria, Zara, Zoe