How to add nav menu items to a specific position within a menu

I’m adding login/logout links to a nav menu using the following code:

function rp_add_login_logout_links( $items, $args ) {

    $link = wp_loginout( get_permalink( get_option( 'woocommerce_myaccount_page_id' ) ), false );

    if ( 'Shop Menu' == $args->menu ) {
        $items .= '<li id="menu-item-login" class="menu-item menu-item-login">' . $link . '</li>';
    }

    return $items;
}
add_filter( 'wp_nav_menu_items', 'rp_add_login_logout_links', 10, 2 );

Since $items is a string, I can really only easily prepend or append the links to the list. I need this link to appear before a certain menu item in the list, it would end up being the third item from the end. Is there another filter or method I could use to accomplish this?

I tried using strpos to find the nav item I was looking for and manipulate the $items string but couldn’t get it to match the menu item HTML.

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Turns out there is a wp_nav_menu_objects filter that allows you to modify the array of nav menu items before they are joined into a string. I was able to accomplish what I needed using the following function:

function wpse121517_add_shop_menu_links( $items, $args ) {

    if ( 'Shop Menu' !== $args->menu )
        return $items;

    // Where to redirect after logging in or out
    $redirect = get_permalink( get_option( 'woocommerce_myaccount_page_id' ) );

    $new_links = array();

    if ( is_user_logged_in() ) {
        $label = 'Logout';
        $link = wp_logout_url( $redirect );

        // Create a nav_menu_item object to hold our link
        // for My Account, only if user is logged-in
        $item = array(
            'title'            => 'Account',
            'menu_item_parent' => 0,
            'ID'               => 'my-account',
            'db_id'            => '',
            'url'              => get_permalink( get_option( 'woocommerce_myaccount_page_id' ) ),
            'classes'          => array( 'menu-item' )
        );

        $new_links[] = (object) $item;  // Add the new menu item to our array
        unset( $item );
    } else {
        $label = 'Login';
        $link = wp_login_url( $redirect );
    }

    // Create a nav_menu_item object to hold our link
    // for login/out
    $item = array(
        'title'            => $label,
        'menu_item_parent' => 0,
        'ID'               => 'loginout',
        'db_id'            => '',
        'url'              => $link,
        'classes'          => array( 'menu-item' )
    );

    $new_links[] = (object) $item; // Add the new menu item to our array
    $index = count( $items ) - 2;  // Insert before the last two items

    // Insert the new links at the appropriate place.
    array_splice( $items, $index, 0, $new_links );

    return $items;
}
add_filter( 'wp_nav_menu_objects', 'wpse121517_add_shop_menu_links', 10, 2 );