I'd go for Lydia, or Violet or Molly as runners up. Of his choices Octavia and Annabel are nice
Three names is fine I think but you don't want it to be too fussy, so something like:
Lydia Jasmine May
Violet Anna Noelle
Octavia Annabel Grace
Annabel Flora Grace
Molly Lydia May
Other names you might like: Cassia, Verity, Flora, Susannah, Jasmine, Hope, Rowan, Robin, Nancy, Estella, Stella, Celeste
Summer, Leigh, Nova, Savannah, Sienna are all a bit Disney meets The Only Way is Essex so I would avoid. Reagan is odd (bringing to mind a dodgy president, a horror movie and a Shakespearian villain) Isla is lovely but very oversued, Lily the same and a bit wet. I think Mae is better spelt May.