You're right about Nebby and Kamehameha, but I could only get them to DoW each other. I couldn't do anything to get them to DoW Haile or Theodora, who were my primary concerns. I'm sure there were things I could've done better.
One thought... in the game, I as the Inca had a DoF with 5 out of 7 AIs, including Haile and Theodora. In your experience, would denouncing Theodora have worked to convince my other 4 friends to denounce her as well? If that worked, then I probably could've bribed a war. I could've waited for my DoF with her to expire to avoid the backstab penalty, but my concern was the "You denounced someone that they like more than you" penalty.
In the end, I needed every single DoF (and subsequent research agreement) to catch up, so any diplomatic penalty would've sunk me. But might that idea have worked? The diplomatic nuances with the AI is one of my weaknesses in Deity games I think.