We'll create fresh WordPress site with 404 Site Checker installed. You have 20 minutes to test the plugin after that site we'll be deleted.
This plugin will look at another site you specify whenever a 404 error occurs and check if the requested path is there. If the path is found, it will redirect there rather than show the WP 404 page.
This is particularly useful to silently redirect over to an archival copy of a website when a major redesign has been done.
More information about this plugin can be found on its homepage.