Server :: Exchanging Data Between Internet And Localhost

I have an Apache 2 server setup in Ubuntu 10.04 LTS on my lab computer. The server listens on port 80, by default. I also have another process listening on port 4000 - this is a special server that executes some Matlab and other application scripts. However, due to university policy (or some licensing/faculty regulation - not really sure), this port 4000 has been set as one that listens only to the localhost. Now, we need to allow a few of the scripts to be run by people remotely.

We tried to setup a web interface - they enter a few values into a HTML form and submit. This form has action="URl... (basically, we were hoping the external form turns data over to the internal form), thereby keeping everyone happy. However, it turns out that this didn't work - the server on port 4000 realizes that the request isn't internal.

What would be the best way of handling it? While we did consider port forwarding, we didn't want everything to be accessible from the internet - i.e. we wanted a tightly controlled interface when accessed from outside, but if someone writes a program on localhost, we want everything to go through as normal (i.e. the current setup). Is there a way to do this without duplication (i.e. setup a new port 5000, that has only the components we want the external users to access)?