Sorry, reading your original question again and maybe you are not using queries within the settings of the board at all.
When you are adding a new story, which 'Project' folder are you scoped to? Could that be limiting your available iterations? The board may display multiple Project folders, but if you are adding a new story it will default to the Project folder to which you are scoped. If you are in the 'Outsourced Projects' folder, then I would only expect you to see the 4 iterations available to that team. Is that the issue?