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

content/browser/renderer_host/render_widget_host_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 CONTENT_BROWSER_RENDERER_HOST_RENDER_WIDGET_HOST_VIEW_MAC_H_
 #define CONTENT_BROWSER_RENDERER_HOST_RENDER_WIDGET_HOST_VIEW_MAC_H_
 #pragma once
 
 #if defined(__OBJC__)
 
@@ skipping 112 matching lines @@
   // Event monitor for gesture-end events.
   id endGestureMonitor_;
 }
 
 @property(nonatomic, readonly) NSRange selectedRange;
 
 - (void)setCanBeKeyView:(BOOL)can;
 - (void)setTakesFocusOnlyOnMouseDown:(BOOL)b;
 - (void)setCloseOnDeactivate:(BOOL)b;
 - (void)setToolTipAtMousePoint:(NSString *)string;
-// 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;
-// Notify the RenderWidgetHost that the frame was updated so it can resize
-// its contents.
-- (void)renderWidgetHostWasResized;
 // Cancel ongoing composition (abandon the marked text).
 - (void)cancelComposition;
 // Confirm ongoing composition.
 - (void)confirmComposition;
 // Enables or disables plugin IME.
 - (void)setPluginImeActive:(BOOL)active;
 // Updates the current plugin focus state.
 - (void)pluginFocusChanged:(BOOL)focused forPlugin:(int)pluginId;
 // Evaluates the event in the context of plugin IME, if plugin IME is enabled.
 // Returns YES if the event was handled.
@@ skipping 273 matching lines @@
 
 class RenderWidgetHostView;
 class RenderWidgetHost;
 
 namespace render_widget_host_view_mac {
 CONTENT_EXPORT RenderWidgetHostView* CreateRenderWidgetHostView(
     RenderWidgetHost* widget);
 }
 
 #endif  // CONTENT_BROWSER_RENDERER_HOST_RENDER_WIDGET_HOST_VIEW_MAC_H_