I like
Eve more than
Eva... but I would still rather see it as a nn to
Evelyn. I could see
Eve as a mn to something though and it wouldn't seen as lacking (and it could go with everything - well... not
Evelyn Eve or anything, lol).
Examples (picking from your list):
Abigail EveCharlotte EveHelena EveIsabella EveGreta Eve
Evelyn MoiraEvelyn RosalieEvelyn Greta
"We can even learn from our enemies." -Ovid
Mitakuye Oyasin