Well, here's what I ended up doing:
I created an initFlash function that reads the URL for the current page, and passes the value to a variable in the Flash movie.
<script language = "JavaScript">
<!--
function initFlash(){
window.document.varTest2.SetVariable("varTest", window.location);
}
//-->
</script>
Then, I call the initFlash function from the HTML onLoad event.
<BODY bgcolor="#CCCCFF" onLoad="initFlash()">
It seems like there ought to be a better way, but this is working!