How to add a custom working Shipping Method in WooCommerce 3

I have successfully created a new shipping method and given it support for shipping zones. However when I come to select the method from the dropdown to add it to the zone it does not appear in the 'selected methods list'.

I recorded a screencast gif to demonstrate:

I can't for the life of me figure out why it's not working. It works fine if I select one of the standard methods (Screencast GIF)

Anyone know what's going on here and how to get it to work?

Here's the code that I have from this official thread: Shipping Method API:

if ( in_array( 'woocommerce/woocommerce.php', apply_filters( 'active_plugins', get_option( 'active_plugins' ) ) ) ) {

    function request_a_shipping_quote_init() {
        if ( ! class_exists( 'WC_Request_Shipping_Quote_Method' ) ) {
            class WC_Request_Shipping_Quote_Method extends WC_Shipping_Method {
                /**
                 * Constructor for your shipping class
                 *
                 * @access public
                 * @return void
                 */
                public function __construct() {
                    $this->id                 = 'request_a_shipping_quote'; // Id for your shipping method. Should be uunique.
                    $this->method_title       = __( 'Request a Shipping Quote' );  // Title shown in admin
                    $this->method_description = __( 'Shipping method to be used where the exact shipping amount needs to be quoted' ); // Description shown in admin

                    $this->title = "Request a Shipping Quote"; // This can be added as an setting but for this example its forced.

                    $this->supports = array(
                        'shipping-zones'
                    );

                    $this->init();
                }

                /**
                 * Init your settings
                 *
                 * @access public
                 * @return void
                 */
                function init() {
                    // Load the settings API
                    $this->init_form_fields(); // This is part of the settings API. Override the method to add your own settings
                    $this->init_settings(); // This is part of the settings API. Loads settings you previously init.

                    // Save settings in admin if you have any defined
                    add_action( 'woocommerce_update_options_shipping_' . $this->id, array( $this, 'process_admin_options' ) );
                }

                function init_form_fields() {

                    $this->form_fields = array(

                        'enabled' => array(
                            'title'       => __( 'Enable', 'dc_raq' ),
                            'type'        => 'checkbox',
                            'description' => __( 'Enable this shipping method.', 'dc_raq' ),
                            'default'     => 'yes'
                        ),

                        'title' => array(
                            'title'       => __( 'Title', 'dc_raq' ),
                            'type'        => 'text',
                            'description' => __( 'Title to be displayed on site', 'dc_raq' ),
                            'default'     => __( 'Request a Quote', 'dc_raq' )
                        ),

                    );

                }

                /**
                 * calculate_shipping function.
                 *
                 * @access public
                 *
                 * @param mixed $package
                 *
                 * @return void
                 */

                public function calculate_shipping( $packages = array() ) {
                    $rate = array(
                        'id'       => $this->id,
                        'label'    => $this->title,
                        'cost'     => '0.00',
                        'calc_tax' => 'per_item'
                    );

                    // Register the rate
                    $this->add_rate( $rate );
                }
            }
        }
    }

    add_action( 'woocommerce_shipping_init', 'request_a_shipping_quote_init' );

    function request_shipping_quote_shipping_method( $methods ) {
        $methods['request_shipping_quote_shipping_method'] = 'WC_Request_Shipping_Quote_Method';

        return $methods;
    }

    add_filter( 'woocommerce_shipping_methods', 'request_shipping_quote_shipping_method' );
}

The method key on "woocommerce_shipping_methods" should match the shipping method id

In your case: You should change

function request_shipping_quote_shipping_method( $methods ) {
    $methods['request_shipping_quote_shipping_method'] = 'WC_Request_Shipping_Quote_Method';

    return $methods;
}

add_filter( 'woocommerce_shipping_methods', 'request_shipping_quote_shipping_method' );

To:

function request_shipping_quote_shipping_method( $methods ) {
    $methods['request_a_shipping_quote'] = 'WC_Request_Shipping_Quote_Method';

    return $methods;
}

add_filter( 'woocommerce_shipping_methods', 'request_shipping_quote_shipping_method' );