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

chrome/browser/extensions/browser_action_apitest.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 "build/build_config.h"
 
 #if defined(TOOLKIT_GTK)
 #include <gtk/gtk.h>
 #endif
 
@@ skipping 20 matching lines @@
   virtual ~BrowserActionApiTest() {}
 
  protected:
   BrowserActionTestUtil GetBrowserActionsBar() {
     return BrowserActionTestUtil(browser());
   }
 
   bool OpenPopup(int index) {
     ResultCatcher catcher;
     ui_test_utils::WindowedNotificationObserver popup_observer(
-        chrome::NOTIFICATION_EXTENSION_POPUP_VIEW_READY,
+        content::NOTIFICATION_LOAD_COMPLETED_MAIN_FRAME,
         content::NotificationService::AllSources());
     GetBrowserActionsBar().Press(index);
     popup_observer.Wait();
     EXPECT_TRUE(catcher.GetNextResult()) << catcher.message();
     return GetBrowserActionsBar().HasPopup();
   }
 };
 
 IN_PROC_BROWSER_TEST_F(BrowserActionApiTest, Basic) {
   ASSERT_TRUE(test_server()->Start());
@@ skipping 353 matching lines @@
       BrowserActionExecuted(
           browser()->profile(), action->extension_id(), browser());
 
   // It can take a moment for the background page to actually get destroyed
   // so we wait for the notification before checking that it's really gone
   // and the badge text has been set.
   host_destroyed_observer.Wait();
   ASSERT_FALSE(manager->GetBackgroundHostForExtension(extension->id()));
   ASSERT_EQ("X", action->GetBadgeText(ExtensionAction::kDefaultTabId));
 }