I'm selling a plugin that would enable to use Custom Post Type as "product" of WooCommerce. I did a lot of work on that to make it compatible with WooCommerce 3.0
But here is the most important part.
You have to create your own data store, like this:  
first create a class that extends to WC_Product_Data_Store_CPT. The idea is to overwrite the existing function of this class that check the post type. I found read and get_product_type that does the checking.
class WCCPT_Product_Data_Store_CPT extends WC_Product_Data_Store_CPT {
    /**
     * Method to read a product from the database.
     * @param WC_Product
     */
    public function read( &$product ) {
        $product->set_defaults();
        if ( ! $product->get_id() || ! ( $post_object = get_post( $product->get_id() ) ) || ! in_array( $post_object->post_type, array( 'birds', 'product' ) ) ) { // change birds with your post type
            throw new Exception( __( 'Invalid product.', 'woocommerce' ) );
        }
        $id = $product->get_id();
        $product->set_props( array(
            'name'              => $post_object->post_title,
            'slug'              => $post_object->post_name,
            'date_created'      => 0 < $post_object->post_date_gmt ? wc_string_to_timestamp( $post_object->post_date_gmt ) : null,
            'date_modified'     => 0 < $post_object->post_modified_gmt ? wc_string_to_timestamp( $post_object->post_modified_gmt ) : null,
            'status'            => $post_object->post_status,
            'description'       => $post_object->post_content,
            'short_description' => $post_object->post_excerpt,
            'parent_id'         => $post_object->post_parent,
            'menu_order'        => $post_object->menu_order,
            'reviews_allowed'   => 'open' === $post_object->comment_status,
        ) );
        $this->read_attributes( $product );
        $this->read_downloads( $product );
        $this->read_visibility( $product );
        $this->read_product_data( $product );
        $this->read_extra_data( $product );
        $product->set_object_read( true );
    }
    /**
     * Get the product type based on product ID.
     *
     * @since 3.0.0
     * @param int $product_id
     * @return bool|string
     */
    public function get_product_type( $product_id ) {
        $post_type = get_post_type( $product_id );
        if ( 'product_variation' === $post_type ) {
            return 'variation';
        } elseif ( in_array( $post_type, array( 'birds', 'product' ) ) ) { // change birds with your post type
            $terms = get_the_terms( $product_id, 'product_type' );
            return ! empty( $terms ) ? sanitize_title( current( $terms )->name ) : 'simple';
        } else {
            return false;
        }
    }
}
after that, add a filter to woocommerce_data_stores and use your class.
add_filter( 'woocommerce_data_stores', 'woocommerce_data_stores' );
function woocommerce_data_stores ( $stores ) {      
    $stores['product'] = 'WCCPT_Product_Data_Store_CPT';
    return $stores;
}
with that, you'll be able to add a post type of birds to cart. But will not actually be a success add to cart. Because there's no price, cart will reject it.

To solve that, you need another filter. Below is a simple way of adding the price. 
add_filter('woocommerce_product_get_price', 'woocommerce_product_get_price', 10, 2 );
function woocommerce_product_get_price( $price, $product ) {
    if ($product->get_id() == 815 ) {
        $price = 10;        
    }
    return $price;
}
Once that's done, you'll have success adding to cart.
