The support ticket the Rackspace Cloud guys made sums it up the best, so here is the problem:
A simple (echo) PHP script is behaving differently on a Cloud Server compared to its original location:

Original - http://textspyder.com/chico/findSchedule.php
Cloud Server - http://50.56.81.54/test.php

The script:

# nano /home/andrew/public_html/test.php
Added:
</table width='900'>
<?php
$i=1;
while($i<=500000)
{
echo $i ." ";
$i++;
}
?>
</table>

Apache config update:

Changed: DocumentRoot /var/www > DocumentRoot /home/andrew/public_html
Changed: <Directory /var/www/> > <Directory /home/andrew/public_html/>

When 'implicit_flush' is on php.ini, the script behaves as it should. This is considered unnecessary, and simply a stop-gap solution
'output_buffering' is off, as well as compression (gzipping) on the server itself.

Similar behaviour is encountered with lighttpd.