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

chrome/browser/task_manager/task_manager.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.h"
 
 #include "base/compiler_specific.h"
 #include "base/i18n/number_formatting.h"
 #include "base/i18n/rtl.h"
 #include "base/process_util.h"
@@ skipping 1086 matching lines @@
 
 // Counts the number of extension background pages associated with this profile.
 int CountExtensionBackgroundPagesForProfile(Profile* profile) {
   int count = 0;
   ExtensionProcessManager* manager = profile->GetExtensionProcessManager();
   if (!manager)
     return count;
   for (ExtensionProcessManager::const_iterator iter = manager->begin();
        iter != manager->end();
        ++iter) {
-    if ((*iter)->GetRenderViewType() ==
+    if ((*iter)->extension_host_type() ==
         chrome::VIEW_TYPE_EXTENSION_BACKGROUND_PAGE) {
       count++;
     }
   }
   return count;
 }
 
 }  // namespace
 
 // static
@@ skipping 18 matching lines @@
     // Count the number of extensions with background pages (including
     // incognito).
     count += CountExtensionBackgroundPagesForProfile(profile);
     if (profile->HasOffTheRecordProfile()) {
       count += CountExtensionBackgroundPagesForProfile(
           profile->GetOffTheRecordProfile());
     }
   }
   return count;
 }