Mapping the external IP to the internal one works for me, but have you run
the winhttp proxy configuration utility? (proxycfg) , you have to do that.
Go from a command line to the Sharepoint Portal server\Bin directory and
enter a command like: proxycfg -d -p fake-proxy-name:80 "<local>;*"
Depending on what you need, so be careful. Here's the full details on this
tool

http://msdn.microsoft.com/library/default.asp?url=/library/en-us/xmlsdk30/ht
m/serverxmlhttpproxy.asp

As regards not using a FQDN, I've read a few posts saying this creates
problems, but I'd check that out, I've only ever done it with them,



proxycfg -d -p fake_proxy_name:80 "*.server_name.com;<local>"

You can also enter the settings in Internet Explorer on the Server and using the -u switch: proxycfg -u

Restart the server