Using your CMS to create new content does produce the correct code (i.e. 'cms'):
<?php
include('/domains/55886/web/cms/WA_CMS/addtosite.php');
echo WA_getCMSContent($database_localhost, $localhost, 'test' , 'test');
?>
As it seems to be recognising that correctly, it may be easiest and safest to just change your CSSMenuWriter/cssmw/menu.php file by changing the 2nd and 3rd lines from:
$WA_localRoot = "".$WAGLOBAL_localRoot."";
$WA_remoteRoot = "".$WAGLOBAL_remoteRoot."";
to:
$WA_localRoot = "/cms/";
$WA_remoteRoot = "/cms/";