I definitely think Lark Rosalie is the best choice out of your list! I adore Birdie, and think this combo would really be special for you.
I know you said that you don’t like a lot of the more common full names for Birdie, but I thought I’d drop a few just in case. Personally, I feel she works as a nickname to any B name (so Beatrix, Bernadette, Beverly, Beulah, etc.), but I know that a lot of those don’t have the whimsy it seems you’re looking for!
Maybe you’d like Florence? I’ve always loved Birdie as a nickname for her, and she feels quite feminine and whimsical. Along the non-b name wave, perhaps…
Paloma – means dove
Roberta – from the “bert” sound
Linnet – a type of bird
Wren – type of bird
Alberta – from the “bert” sound (love this with H and W’s names!)
Aya – Hebrew word for bird (?)
Avis – means bird in Latin
Mavis – means songbird
Liberty – from the “bert” sound (I love this with Holiday and Winry!)
Phoebe – a type of bird