Honestly I'm not all that thrilled with introducing a secret society of insane but professional killers. Just feels too fantastical to me. I can see some bad like minded people who group together but not really an illuminati type scenario. Just doesn't ring true or realistic to me. Personally, I'm more interested in playing this realistically. Ordinary people in a very unordinary situation. Dead people walking around eating other people IS the twist, the fantastical element. Introducing additional fantasy, in my mind, is unnecessary and changes the whole thread for me. There are enough problems and conflicts when playing it straight and, for me, that's a more interesting story.
Just my two cents. Without an active "game master" as blue iris seems to have lost interest a long time ago, it's sort of a free for all or loose democracy on the story line. If the majority wants to go with the secret group then that's the way it should go. However, I don't find it very realistic that my character would last a single encounter with the sort of folks it seems like you're wanting to introduce. As I said, he's just an ordinary person trying to survive in an unordinary world. He's not a trained killer who fights well organized secret societies of psychopathic murderers. In other words, I don't expect him to make it. Which is fine. Just a heads up from my corner.