wp_logout problem

You could create a custom Page template which contains only the logout code, no call to header.php etc. When you load the /member-logout/ page you’re probably calling the default page.php template which is loading header.php etc. If instead you apply your custom Page template it will just perform the logout action and can then redirect, as no headers have been sent (headers being different than just header.php but as soon as you output any HTML, which is contained in header.php, you have headers which is preventing the redirect).