I'm glad you like it and satchat.amsat.org would probably be a worthwhile place for it to be to attract traffic.
Server cost is not an issue, as it currently shares space with other projects. A CNAME DNS entry could be created by AMSAT so that the name "satchat.amsat.org" points to a server that the chat maintainers completely control. This is the modern way to delegate operations such as this. The old way of collecting programs on a single server can lead to delays over system admin tasks, explaining and documenting what is to be done, etc, that can be dispensed with in a simpler hobbyist environment.
The underlying system is Linux, but it is not apache/PHP. The technology stack is Linux/NGINX/MeteorJS/MongoDB/Predict (yes, the old Linux text-based predictor runs under the hood and gets dumped to the database) and is more flexible for building real time systems such as chat. Meteor has also made a reputation as a new way to do rapid prototyping of web apps, see: www.meteor.com
I believe it can be made reasonably secure, and low-maintenance, except for certain human factors -- for which "control operators" or moderators could be worthwhile to watch for the occasional riff-raff.
Also, I have ideas for several features which I haven't put into code yet, like a tool to figure out skeds between two people, or a tool for DX to announce when they might be on. Cooperative/competitive map building for the weather sats. It is possible to make a fair (but not great) weather sat map collector with a $20 usb dongle, completely free (and hackable) software, PVC end cap turnstile antenna, and $100 Linux pc and no ham license whatsoever (and thus, a kids/beginner project kit might be born). Occasionally the fair setup makes nice pictures, that with some filters might be uploaded somewhere automatically. Imagine 20-30 hobbyists doing that effortlessly. It could even catch on. Libraries of sound recordings of the ham birds is a little more expensive but not that much harder, and is certainly also doable.
Anyway, I suggest we followup by email and see where this goes.
73 Paul KI6CQdrpaulbrewer@email@example.com