And as it usually happens, I find the answer a few minutes after posting the question…
So here’s what I did in my theme’s functions.php file to solve my problem:
function modify_products() {
if ( post_type_exists( 'product' ) ) {
/* Give products hierarchy (for house plans) */
global $wp_post_types, $wp_rewrite;
$wp_post_types['product']->hierarchical = true;
$args = $wp_post_types['product'];
$wp_rewrite->add_rewrite_tag("%product%", '(.+?)', $args->query_var ? "{$args->query_var}=" : "post_type=product&name=");
add_post_type_support('product','page-attributes');
}
}
add_action( 'init', 'modify_products', 1 );
Everything works: hierarchy, rewriting, etc 🙂