Have ExtensionHost use TabContents instead of RenderViewHost. Try #3.

chrome/browser/ui/views/extensions/extension_view.h

Index: chrome/browser/ui/views/extensions/extension_view.h
diff --git a/chrome/browser/ui/views/extensions/extension_view.h b/chrome/browser/ui/views/extensions/extension_view.h
index e399658f6584ef2516c77585619e8260e0d31b96..1a41bb67b5a20c7ae1ea1b51c3839d8e7f5c9909 100644
--- a/chrome/browser/ui/views/extensions/extension_view.h
+++ b/chrome/browser/ui/views/extensions/extension_view.h
@@ -28,9 +28,6 @@ class ExtensionView : public views::NativeViewHost {
   class Container {
    public:
     virtual ~Container() {}
-    // Mouse event notifications from the view. (useful for hover UI).
-    virtual void OnExtensionMouseMove(ExtensionView* view) = 0;
-    virtual void OnExtensionMouseLeave(ExtensionView* view) = 0;
     virtual void OnExtensionPreferredSizeChanged(ExtensionView* view) {}
   };
 
@@ -43,8 +40,6 @@ class ExtensionView : public views::NativeViewHost {
 
   // Notification from ExtensionHost.
   void UpdatePreferredSize(const gfx::Size& new_size);
-  void HandleMouseMove();
-  void HandleMouseLeave();
 
   // Method for the ExtensionHost to notify us when the RenderViewHost has a
   // connection.