You can use something like this in the quote function:
Code:
          $cost = preg_replace('/[^0-9.]/', '',  $cost);

// bof: skip shipping method type based on amount
          $skip_method = false;
          $order_total_amount = $_SESSION['cart']->show_total() - $_SESSION['cart']->free_shipping_prices();
// echo 'Type: ' . $type . '<br>';          
          if ($order_total_amount > 8 && $type == 'First-Class Mail International Letter') {
            $skip_method = true;
          }
          if ($skip_method) { 
            // do not show
          } else {
          $methods[] = array('id' => $type,
                             'title' => $title,
                             'cost' => ($cost * $shipping_num_boxes) + (MODULE_SHIPPING_USPS_HANDLING_METHOD == 'Box' ? MODULE_SHIPPING_USPS_HANDLING * $shipping_num_boxes : MODULE_SHIPPING_USPS_HANDLING) );
          }
// eof: skip shipping method type based on amount
        }

        $this->quotes['methods'] = $methods;
You can uncomment the echo line to see for sure what your type is on the shipping that you want to make disappear ... it has to be exactly the same ...

The code in red is the new code ...