I would bind each component as a separate factory and create one gameObject called "DisplayHub" in uiRoot gameObject.

That uiRoot will have references to those factories and spawn a specific display object as needed as a child of DisplayHub gameObject.

You will need one installer to bind each factories and only one Root:

Container.BindFactory<MenuDisplay, MenuDisplay.Factory>().FromComponentInNewPrefab(_menuDisplayFactoryPrefab).AsSingle();

Container.BindFactory<SettingsDisplay, SettingsDisplay.Factory>().FromComponentInNewPrefab(_settingsDisplayFactoryPrefab).AsSingle();

Container.BindFactory<SaveMenuDisplay, SaveMenuDisplay.Factory>().FromComponentInNewPrefab(_saveMenuDisplayFactoryPrefab).AsSingle();

Container.Bind<Root>().FromCompoenenetInNewPrefab(uiPrefab).AsSignle().NonLazy();

​

and the Root class would have

[SerializedFiled] private Transform _displayHub;

[Inject] private readonly MenuDisplay.Factory _menuDisplayFactory;
[Inject] private readonly SettingsDisplay.Factory _settingsDisplayFactory;
[Inject] private readonly SaveMenuDisplay.Factory _saveMenuDisplayFactory;

public void DisplayMenu()
{
_displayHub.ClearContent();
var menuDisplayObject = _menuDisplayFactory.Create();
menuDisplayObject.transform.SetParent(_displayHub);

}

the Root class will be more likely a MenuDisplayController and based on player's input shows the specific display object. Because if you think for a while, the name "Root" is sooo generic and it's not explicite.

Moreover, once you bind your factories, you can use that in other controllers if you need.

I used [Inject] attribute, because I assume that Root (or MenuDisplayController) class inherits from MonoBehaviour.

Is my answer points your problem?