(Writing this as I watch an episode of Misomer Murders myself)
The first "long form" for
Ed I thought of was
Edith. I also like the
Edna and
Edwina mentions.
If I had to give my daughter a masculine/unisex nickname, I'd probably go with
Charlie (
Charlotte) or
Frankie (
Frances). Fits the masculine-or-unisex vibe while being common enough that it wouldn't seem strange on a girl.