I love the nickname Sephi/Sephie (I prefer the spelling Sephy) and I've even considered using Persephone for it, although I don't like that name! I think it's usable, but not very obvious, for Josephine, and fine for Persephone.
There is also a Persephone nn Sephy in Malorie Blackman's 'Noughts and Crosses' trilogy. I highly recommend the books!