Using wp_insert_post and post_update_meta but need to fire save_post afterward

You should be able to use wp_update_post() –https://codex.wordpress.org/Function_Reference/wp_update_post

Eg.

$my_post = array(
    'ID' => $post_id,
);

wp_update_post( $my_post );

The ‘save_post’ action should run when this function is called.