Moving on...
I had one started (not posted, but first chapter written) where all the characters are either cops or criminals: Gendo is the head of Rokubungi Gumi, Kaji is an undercover cop, Rei is Gendo's 'Daddy's Little Tyke-bomb Hitgirl,' Shinji ends up in the family after Yui's death via custody shenanigans, and Evangelion is a weaponized hallucinogenic (chemical label LCL), the formula having been stolen by the Gumi and being produced as a new drug for street consumption. There's more characterization (for Keel, Asuka, Kaworu, Misato, etc.), but this should do for the outline.
I've been back and forth on whether I should just go ahead and post, or see if anyone else wanted to take a stab at it.
Thoughts?