Further to my above Eureka, as well as extracting the Laravel bare HTML output, I have also used CodeIgniter 3.0 to extract the bare HTML. It is working fine and gets 100% Pingdom Performance Grade.
CodeIgniter:
// RENDER TO SCREEN
$this->load->view( $data['page_new'], $data, FALSE);
// if 200===http_response_code()
// WRITE TO "_CACHE_JJ/current/"
// else
// WRITE TO "_CACHE_JJ/Found"
$this->_new_cache_jj($data, $delete= FALSE);