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

chrome/browser/tab_contents/tab_contents_view_mac.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_TAB_CONTENTS_TAB_CONTENTS_VIEW_MAC_H_
 #define CHROME_BROWSER_TAB_CONTENTS_TAB_CONTENTS_VIEW_MAC_H_
 #pragma once
 
 #if defined(__OBJC__)
 
@@ skipping 24 matching lines @@
 @interface TabContentsViewCocoa : BaseView {
  @private
   TabContentsViewMac* tabContentsView_;  // WEAK; owns us
   scoped_nsobject<WebDragSource> dragSource_;
   scoped_nsobject<WebDragDest> dragDest_;
   scoped_ptr<WebDragBookmarkHandlerMac> bookmarkHandler_;
 }
 
 // Expose this, since sometimes one needs both the NSView and the TabContents.
 - (TabContents*)tabContents;
+
+// Set frame, then notify the RenderWidgetHost that the frame has been changed,
+// but do it in a separate task, using |performSelector:withObject:afterDelay:|.
+// This stops the flickering issue in http://crbug.com/31970
+- (void)setFrameWithDeferredUpdate:(NSRect)frame;
 @end
 
 // Mac-specific implementation of the TabContentsView. It owns an NSView that
 // contains all of the contents of the tab and associated child views.
 class TabContentsViewMac : public TabContentsView {
  public:
   // The corresponding TabContents is passed in the constructor, and manages our
   // lifetime. This doesn't need to be the case, but is this way currently
   // because that's what was easiest when they were split.
   explicit TabContentsViewMac(TabContents* web_contents);
@@ skipping 90 matching lines @@
 
 // Functions that may be accessed from non-Objective-C C/C++ code.
 class TabContents;
 class TabContentsView;
 
 namespace tab_contents_view_mac {
 TabContentsView* CreateTabContentsView(TabContents* tab_contents);
 }
 
 #endif  // CHROME_BROWSER_TAB_CONTENTS_TAB_CONTENTS_VIEW_MAC_H_