Woocommerce custom orderby doesn't work in search results

I've noticed that my custom sorting option works perfectly when browsing the shop but fails in search results. The current code follows many examples available:

// Add "Sort by discount" to sorting options. Defaults to biggest to smallest discount.

add_filter('woocommerce_get_catalog_ordering_args'
          ,'mycode_woocommerce_add_salediscount_to_catalog_ordering_args'
          );

function mycode_woocommerce_add_salediscount_to_catalog_ordering_args( $args ) {
    $orderby_value = isset( $_GET['orderby'] ) 
        ? wc_clean( $_GET['orderby'] ) 
        : apply_filters('woocommerce_default_catalog_orderby'
                       ,get_option('woocommerce_default_catalog_orderby' )
                       );
    if ( 'discount' == $orderby_value ) {
        $args['orderby']    = 'meta_value_num';
        $args['order']      = 'DESC';
        $args['meta_key']   = 'discount_amount';
    }
    return $args;
}

add_filter('woocommerce_default_catalog_orderby_options'
          ,'mycode_woocommerce_add_salediscount_to_catalog_orderby'
          );
add_filter('woocommerce_catalog_orderby'
          ,'mycode_woocommerce_add_salediscount_to_catalog_orderby'
          );

function mycode_woocommerce_add_salediscount_to_catalog_orderby( $sortby ) {
    $sortby['discount'] = __( 'Sort by discount', 'woocommerce' );
    return $sortby;
}

This code I've added to the my_custom_code.php which is a simple plugin for my own code.

It sorts based on a meta value that every product in my store has.

When used on a search results page, instead of the custom ordering, the ordering is the same as 'relevance'.

Looking through the WC code that controls ordering, I see that is_search() is called in multiple places, with ordering reset to 'relevance' but the default sorting options are able to override this and they still work (e.g. sort by price still works).

So I imagine that I need to adjust the code slightly to behave in the same way as the default search options but I can't see how to do this.

Does anyone know?

Thanks!