I will probably get yelled at, but the simple answer to me seems to be writing a web app. It was stated that they are willing to write terminal applications, so there is obviously some programming ability present.

So why not write web apps. If you write your HTML well, then you can run it over pretty low bandwidth and all the work can be done by the server. There are still sites that work with 56k modems so it is possible to create low bandwidth sites (although most have stopped bothering).

There isn't a strong definition of what exactly the goal is and some projects don't lend themselves to being web based, but with a little work most things that can be done through the terminal can be done through the web server with far less bandwidth needed.