Bridget Rosemary "Birdie" - I love this. Birdie is such a cute, old-fashioned nn. I would love to meet a little girl named Birdie.
Cecily Thomasine "Lily" - I'm not a fan of Lily, but the combo is beautiful. I love Cecily and Thomasine is so pretty and unusual in the mn spot.
Mabel Constance "May/Bel" - I love Mabel! It's such a pretty name, and May is an adorable nn. Constance is wonderful as a mn.
Elsa Clementine "Elle/Elsie" - Elsa Catherine is on our short list for a girl. I love it so much. It's cute enough for a little girl, but would work perfectly for a grown woman as well. Elsie is a great nn. I'm not a huge fan of Clementine, but the combo is nice.
Stella Josephine - Stella isn't really my favorite. It reminds me too much of Estelle from Friends. Stella Josephine is a very nice combo, regardless of who the name reminds me of! (:
Leopold Augustus "Leo" - I like this; it feels very regal. I especially like Augustus.
Edmund Clarence - I'm not a huge fan; Teddy would make a cute nn though. (:
Hector Nathaniel - I love Hector; it's very heroic. Nathaniel sounds very handsome with it and balances it out nicely.
Rupert Thaddeus "Rupe/Rupie" - I'm not a fan of either name, but they sound nice together.
Lucian Thomas "Luc" - Lucian isn't my style (I prefer Lucius,) but it sounds nice with Thomas. Luc is a nice nickname.
I think we have very similar taste in girl names, less so in boys. Your list is great, though.
Here are some names you may like:
Adela / Adele
Sylvia / Sylvie
Innes / Ennis
Graham / Graeme
Lewis / Louis
Linden / Lyndon