Using Apache as a Reverse ProxyTurns out that with a few configuration tweaks I can use apache as a reverse proxy. I added the following lines to the bottom of my \Apache2.2\conf\httpd.conf :
Order deny,allow Allow from allProxyPass /stwebapi http://ghprd01:9081/stwebapi ProxyPassReverse /stwebapi http://ghprd01:9081/stwebapi
So now any requests to /stwebapi will be redirected to by apache to http://ghprd01:9081/stwebapi, and as far as the browser knows it all comes from the same domain.
Piece of cake!