We'll create fresh WordPress site with WooCommerce Custom Overlays installed. You have 20 minutes to test the plugin after that site we'll be deleted.
Now your WooCommerce products that are out of stock can be distinguished from in stock products with a dyanmically applied image overlay to all product images that are out of stock. You can use the preloaded pictures included in the plugin, or upload and set your own on the plugin settings page.