Somewhat of a work-around: I put the tab widget itself into a DockWidget, then made a dock widget as before for the dialogs and put them both in the same DockWidgetArea of the main window. This stacks them nicely (though it does mean that the upper toolbars and text edit no longer go all the way across) and is pretty close to the desired result.

To really go all-out, I suppose I could try docking the upper toolbars as well, which would be flexible, but for now, this will do!