Wow, this sounds really great. I'd love to take part.
Thinking about Heros battling each other: If a Hero is chosen for a party which tries to get the item for one of the Houses, the Hero might not want to serve this House at all. So, there could be the situation, that they meet each other on their way back, that they have to fight. And then they should have the opportunity to change sides and turn against their party leader. Even if all questies would choose to collaborate, only one Eubric House would get the item. And I even think this would not happen as there always will be (should be) loyal servants of the respective House on each team.
Imagine all the Role Playing possibilites with mixed teams (esp. with a lot of Neutrals).