Lovely names! I think Peri would be a great nn for Persephone.
I would eliminate Philomena because it's too similar in sound to Athena. If you don't like Callie as a nn, then Calliope has to go too! Penelope is ok but it's going to get popular due to the Kardashian baby. Margaret means "pearl" so I would go with Imogen Pearl for mn's.
Top Three Faves
1 Daphne Imogen Pearl - I think Athena and Daphne would be lovely together!
2 Persephone Imogen Pearl - you can use Perry, Seffi or Eppie as nicknames
3 Ariadne Imogen Pearl - a bold choice
Philippa nn Pippa
Theodora nn Thea
Georgia nn Gigi or Georgie
Evangeline nn Evie
Evadne nn Evie
Phaedra nn Fay
Hermione nn Mimi
Eulalia nn Lally
Flora nn Fleur or Flossie
I really like your list in general (and I love your eldest daughter's name)! Here are my thoughts:
Calliope: I really like this name! Calliope Imogen Pearl would be gorgeous. I do think that Callie is a major possibility, though, so be wary of that; while I do know a Calliope who goes by her full name, people have a tendency to nickname and Callie is very intuitive. Pp's suggestion of Poppy is very cute and I think it could work, though you would have to enforce it. Calliope and Athena is a good sibset.
Ariadne: I don't love Ariadne quite so much. Also, neither Ariadne Margaret nor Ariadne Imogen (particularly this one) has perfect flow IMO. And I'm not one for sibsets that all have the same starting letter, so I would nix Ariadne & Athena.
Daphne: I like Daphne Imogen Pearl. However, in comparison with some of your other names, I don't love this one as much. It's still a beautiful name, though, and Daphne and Athena is a good sibset! One aside, Daphne does make Scooby Doo pop into my head. But it's not a terrible association and I'm sure most people won't have it.
Penelope (nn Nell): Love Penelope and LOVE Nell! There is the popularity thing to consider though - but don't let it stop you from using a name you love. I like Penelope Imogen Pearl. If I were you, I might be drawn to a P name because then the first name and second middle would start with the same initial just like older sis and that could be a cute tie. I also really like the flow. This is one of my favorites from your list. Also, Penelope and Athena is great!
Persephone: I think you could definitely steer clear of the nickname Percy. I don't think it's as intuitive as Callie for Calliope, and I also really don't like the nn. I would suggest Sephy or Seph. Persephone Imogen Pearl is gorgeous (can you tell I prefer Imogen to Margaret? I just love how it sounds with your names). My only hangup is that Persephone and Athena are both relatively major goddesses and you could be boxing yourself into a theme. But it is a good sibset!
Philomena (nn Mena): Like the nickname Mena, don't love the name Philomena. I would prefer Philomena Margaret Pearl, but I think Philomena & Athena is just way too matchy because the names rhyme. I'd nix this too.
In order, I like:
1. Penelope or Persephone (can't pick!)
Good luck! You have some gorgeous names to choose from!
I LOVE all of your possibilities [apart from Daphne but that is just personal pickiness]. I would not use Calliope if you don't like the nn Callie but if trained then Persephone could be Sepphie or Penny quite easily. I LOVE the middle names also so overall I would not be worried at all as each of your names would be perfect!
A nickname for Persephone could be Sephy?
I love Daphne!
Thank you all SO much for all the help! Margaret is officially out. It was my partner's suggestion (his grandmother) and I never even thought about the meaning. We will use Imogen Pearl for the middles, which I'm thrilled about because Imogen has been a favorite of mine for a very long time. Philomena is also out - too matchy.
valentine - I LOVE Delphine! He doesn't care for it though so unfortunately it's not an option.
ysaline - my niece's name is Maia so we can't use this one either.
mischa - love your suggestions, especially Hermione! I can't believe I didn't already have this one on my list.
We've narrowed it down to three: Daphne, Persephone (nn Seffi) and Hermione. It's not one definite pick but it is a start, so thank you for the guidance!
Calliope -- I can go either way. Hard to picture another nickname. Cal? Cappie? No idea.
Ariadne -- Favorite. Love love love. Exciting but not too over the top.
Daphne -- Very cute name. Love it.
Penelope (nn Nell) -- Cute. Not my fave, but a good name.
Persephone (dislike Percy as a nn as well, are there any other nicknames?) -- Don't really love Persephone's mythology, and I also feel like it's the best known... Not in love.
Philomena (nn Mena) -- I knew a girl named Philly (short for Philomena) who I did not like and so my judgment is impaired.
Favorites are Ariadne and Daphne. Best of luck!!