Mixing a CocosSharp game with UIViewControllers

Question

I'm creating a CocosSharp game with several additional native screens which I'm going to implement using native iOS UIViewController. The flow is the following:

1. On app startup I'm creating UINavigationViewController and initial view with my custom main menu:

   public override void FinishedLaunching(UIApplication app)
   {
       MainWindow = new UIWindow(UIScreen.MainScreen.Bounds);
       var rootViewStoryboard = UIStoryboard.FromName("GameMenu", null);
       var rootView = rootViewStoryboard.InstantiateViewController("GameMenu");
       var navigationController = new UINavigationController(rootView);
       MainWindow.RootViewController = navigationController;
       MainWindow.MakeKeyAndVisible();
   }
   
   public partial class GameMenu : UIViewController
   {
       public GameMenu(IntPtr handle)
           : base(handle)
       {
       }
   
       public override void ViewDidLoad()
       {
           base.ViewDidLoad();
           btnStartGame.TouchUpInside += (sender, e) => NavigationController.PresentViewController(new GameScene(), false);
       }
   }
   

2. One of the actions leads to another UIViewController (modal) where CocosSharp game is created:

   public partial class GameScene : UIViewController { public GameScene() { }

   public override void ViewDidLoad()
   {
       base.ViewDidLoad();
       _application = new CCApplication();
       _application.ApplicationDelegate = new GameAppDelegate();
       _application.StartGame();
       _application.MainWindow.DisplayStats = true;
   
       OnStopGame();
   }
   

   }

3. Finally on certain event (in my case in 5 sec) I'm trying to finish a game and return back to the main menu:

   public async Task OnStopGame()
   {
      await Task.Delay(5000);
      _application.ExitGame();
      NavigationController.DismissViewController(false, null);
   }
   

As a result I get empty black screen, background music continue to run, no main menu is displayed.

How should I properly navigate from CocosSharp game to a native controller and back? Can they live in parallel?