I like
Penelope. Another nickname could be
Nell. I hate the others.
Pepper is a seasoning and a cartoon character and
Poppy is an old man and one easy typo away from your daughter wearing a school id that says poopy. I like
Piper better. I wonder why you don’t like it since it fits this pattern so well. What about
Pippa,
Pepita,
Perpetua,
Pip,
Pippi, or Pepa?