add a hidden element to the form, and add a javascript on change event to the select list to save the label of the select to the hidden element
onChange="document.form1.hiddenfield.value = document.form1. shipSelect[document.form1. shipSelect.selectedIndex].text"
This example assumes the hidden element is named hiddenfield and the form is named form1
add another set session value behavior to store the hidden element in a session:
<?php
if (!session_id()) session_start();
if($_SERVER["REQUEST_METHOD"] == "POST") {
$_SESSION["eCartCheckoutForm_shipping_method_label"] = "".((isset($_POST["hiddenfield"]))?$_POST["hiddenfield"]:"") ."";
}
?>
and use the eCartCheckoutForm_shipping_method_label session to store the selected shipping method.