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I've never actually heard it used for Penelope, but I asked about it myself recently when I wanted other NN's for Penelope than Penny. I think it could work, because I agree that Poppy sounds nicknamey, and as such I think you could use it quite freely.
How about for Philippa?
Pomona, Philomena, Pandora, Portia...
Peony and Primrose would be kind of silly since they're other flowers.