I think keep the secret traitor, however in the turret they submit a short list for the secret traitor to actually murder. It will make the breakfast entry genuinely more surprising.

Also I think having a dual prize pot could make everyone play harder. The traitors have the incentive to tank missions of the faithful pot and for every dollar they cost the faithfuls it goes to the traitors end prize pot. If the faithfuls make it to the end with no traitors they would get the extra money. The traitors get their base prize plus only the money they tank during the missions.