Have you ever seen something like this done on FB before? It sounds to me like FBJS is causing you the problem with its lack of API options.
One way to do it in normal JS is to get the position of the sliders, both Right and bottom, and also the whole screen size, and then determine where the center of the viewable window is based on the full frame size and the slider offsets.
All of those variables should be defined or be retrievable via javascript for you to grab and manipulate, and then it is simply updating the css values on a div to move the window to the correct location. you can then poll the state of the window sliders or monitor their event and retrieve their position as it is updated to recalculate the center of the window.
If FBJS has no facility to determine window size or slider position, then you have a much harder problem on your hands.