Alright, so... the topic pretty much explains what I'm looking to do here.
Ginji would probably work best as a warlock, reflavored for lightning. Seriously, it might just work.
Ban would be more... complicated. His Jagan is simply something I haven't seen in D&D. And then there's the fact he's a Spring Attacking ubercharger.
Himiko might work as a potion-throwing rogue with actual potions.
Shido is... umm... a Totemist? A Binder? Hell if I know.
Kazuki is a Sorcerer who forgot any utility spells in the seat of his androgynous other pants.
Obviously, this is just the beginning, and needs lots of work. Any ideas?