Not big on White Rabbit. Simply because whenever DC and Marvel have too similar characters, when one is made prominent in a media adaptation, the other is deliberately downplayed and marginalized. Eg. Treatment of Marvel's Enchantress after DC's Enchantress featured in the
Suicide Squad movie, Sony's loong reluctance to feature Black Cat, the most prominent female Spidey villain in the movies (Raimi reportedly even wanted to change her into Vulturess for a planned
Spider-Man 4), and even now when they are finally planning to feature her in a spin-off, they've tacked Silver Sable of all characters on to her. After
Aquaman the movie comes out, I doubt Marvel will have plans for Namor and his version of Atlantis for the big screen either.
I propose the unsettlingly creepy Jane Doe instead. But only the original version in Dan Slott's
Arkham Asylum: Living Hell. Not the ruined subsequent appearances.
Speaking of
Living Hell, it had a rare interesting showing for Magpie as well, even establishing a proto-Harley relationship of sorts for her with Ivy in the story.
The Anchoress can also work very well if used as a villain exclusive to Arkham based stories. She will add to Arkham Asylum's Gothic atmosphere.