How to make Prodigy web-server serve content publicly for a team

Yes, that should work. Also make sure that the port you're serving on can be accessed from the outside (sometimes 8080 is blocked by default, so you'll have to change that). It's also possible that AWS wants you to set the host to * on AWS – see this thread:

If you want a more flexible solution, you can also run Prodigy behind a reverse proxy.