Part of my problem with coming up with a group character for GodWar is the game is not much focused on material advancement. The assumed character archetypes are for the most part out and out heroic, and the whole game is about fighting to protect the fate of humanity. This doesn't leave a lot of team focus for lining your pockets, gathering political power, etc (or in other words a lot of the facets that make the Song of Ice and Fire and Reign systems work so well). While obviously one can collect material wealth and political power for altruistic, world savings ends (so you can build your steam robot to defend Barcelona from the blood citadel known as the Parliament of Slaughter), it does not come as easy when your goal is the advancement of your house, mercenary company, etc. Also money grubbing templars, while possessing a certain amount of historical accuracy, don't really seem like awesome characters to play compared to demon smashing templars.
So basically I am concerned that I am trying to shoe horn a system into a game that does not need it. I could excise the group character system, but I really like that sort of mechanic. I could work on Last Knights of Camelot since it easily includes a group character mechanic, but I don't think my prospective group digs giant robots that much. Shadow of Azathoth is off the table for now. I've been itching to try and run a post-apocalyptic game, but that genre has seen a lot of games of late, and good ones of that. I'm not sure I'd have something to say with that game that Gamma World, Apocalypse World, Atomic Highway, or Barbarians of the Aftermath hasn't already said.