Have ExtensionHost use TabContents instead of RenderViewHost. Try #2. The first

chrome/browser/task_manager/task_manager_resource_providers.cc

 // 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.
 
 #include "chrome/browser/task_manager/task_manager_resource_providers.h"
 
 #include <string>
 
 #include "base/basictypes.h"
 #include "base/file_version_info.h"
@@ skipping 1109 matching lines @@
 
 void TaskManagerExtensionProcessResource::SetSupportNetworkUsage() {
   NOTREACHED();
 }
 
 const Extension* TaskManagerExtensionProcessResource::GetExtension() const {
   return extension_host_->extension();
 }
 
 bool TaskManagerExtensionProcessResource::IsBackground() const {
-  return extension_host_->GetRenderViewType() ==
+  return extension_host_->extension_host_type() ==
       chrome::VIEW_TYPE_EXTENSION_BACKGROUND_PAGE;
 }
 
 ////////////////////////////////////////////////////////////////////////////////
 // TaskManagerExtensionProcessResourceProvider class
 ////////////////////////////////////////////////////////////////////////////////
 
 TaskManagerExtensionProcessResourceProvider::
     TaskManagerExtensionProcessResourceProvider(TaskManager* task_manager)
     : task_manager_(task_manager),
@@ skipping 260 matching lines @@
 
   return &resource_;
 }
 
 void TaskManagerBrowserProcessResourceProvider::StartUpdating() {
   task_manager_->AddResource(&resource_);
 }
 
 void TaskManagerBrowserProcessResourceProvider::StopUpdating() {
 }