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

chrome/browser/ui/gtk/extensions/extension_view_gtk.h

 // Copyright (c) 2011 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 #ifndef CHROME_BROWSER_UI_GTK_EXTENSIONS_EXTENSION_VIEW_GTK_H_
 #define CHROME_BROWSER_UI_GTK_EXTENSIONS_EXTENSION_VIEW_GTK_H_
 #pragma once
 
 #include "base/basictypes.h"
 #include "third_party/skia/include/core/SkBitmap.h"
@@ skipping 37 matching lines @@
 
   RenderViewHost* render_view_host() const;
 
  private:
   void CreateWidgetHostView();
 
   Browser* browser_;
 
   ExtensionHost* extension_host_;
 
-  RenderWidgetHostViewGtk* render_widget_host_view_;
-
   // The background the view should have once it is initialized. This is set
   // when the view has a custom background, but hasn't been initialized yet.
   SkBitmap pending_background_;
 
   // This view's container.
   Container* container_;
 
   DISALLOW_COPY_AND_ASSIGN(ExtensionViewGtk);
 };
 
 #endif  // CHROME_BROWSER_UI_GTK_EXTENSIONS_EXTENSION_VIEW_GTK_H_