Welcome to the club. Unfortunately Paul is absolutely correct: you're stuck. We have Sony NX5Us and one X70 and they behave in the manner you describe. Where I disagree with him is in the suggestion that no "proper" cameras have the feature you're asking for. I have two Sony PD150s that have total iris control, from f18 through f11. These cameras, and their cousin the PD170 provide zooming at will through any iris setting, up and down the range, without affecting the the iris at all. In manual mode the gain is locked in to whatever setting you have chosen and is unaffected by the iris.
For my money the PD150/170 has long been one of the best cameras below the $5000 price point for shooting theatrical events as they allow the operator to match the light levels provided by the theatre's lighting designer. Regrettably they only shoot in DV.