I don't think that nicknames need to be a direct derivative of the existing name, which really opens up the options.
Allegra - This is my mom's name, so I am happy to see it on your list. She has always gone by her full name, and I don't think there are a lot of natural nicknames in this case.
Calista - Callie/Cali, Lissy,
Lili (LeeLee)
Juliet - Jet, Julie/Jewel,
Lia,
Jules
Sapphira - I have no idea for this one! Me either!
Valentina - Lenni,
Tia,
Allie
Seraphina - Phina,
Nia, Fia,