Here is an update from a WPEngine engineer; any clues on your end? I doubt the below is the exact scenario, but you may have some ideas. Thanks…Jim P.
According to the HTTP Status code index, a 408 response means “server timed out waiting for the request”. That means that the browser took too long to send the data, and the server gave up waiting for it.
I’m not familiar enough with the plugin to know exactly what is happening, but is it possible that the plugin is attempting to send a very large amount of data to the server, and so the timeout is reached before the browser can send it?