Well what I suggest is using the techniques used to find xss exploits. What would seem to be happening over at worldpay is that they suck the page through and knock off the <base href tag from header_php.php so what you could do is some of these combinations in your file and see if you can fool the part of their program that recognises the tag.
First of all you need to be 100% positive you are editing the correct file for your layout. the default is at
includes/templates/template_default/common/html_header.php
so if you put
<!--hello world-->
in that page then you should see it appear on worldpay's suck through page, otherwise you look for other header files in your template overrride structure
then you would replace the line
<base href="<?php echo (($request_type == 'SSL') ? HTTPS_SERVER . DIR_WS_HTTPS_CATALOG : HTTP_SERVER . DIR_WS_CATALOG ); ?>" />
<base \ href=<?php echo (($request_type == 'SSL') ? HTTPS_SERVER . DIR_WS_HTTPS_CATALOG : HTTP_SERVER . DIR_WS_CATALOG ); ?>" />
or
<base \0 href=<?php echo (($request_type == 'SSL') ? HTTPS_SERVER . DIR_WS_HTTPS_CATALOG : HTTP_SERVER . DIR_WS_CATALOG ); ?>" />
or this should work
<script language="javascript" type="text/javascript">
document.write('<ba'+'se '+'href="');
</script>
<noscript><base href="</noscript><?php echo (($request_type == 'SSL') ? HTTPS_SERVER . DIR_WS_HTTPS_CATALOG : HTTP_SERVER . DIR_WS_CATALOG ); ?>" />
Philip