I think Eggie would be cute, and necessary because the name is very paper-y. So long and heavy. I'm not against long deliberate names - I think they're neat, although not my usual style. But if nicknames were not allowed, I would not think they were too great.
It does remind me of eggs
Florentine, but I don't think that wrecks it. I don't personally care for the sounds in
Eglantine but I don't think it's bad in any way.