Let's say they make it mandatory. Would it be possible for a group of people with one having unfettered access because, say, they cross the border all the time to a place that has full Internet, and they use wget to tar/gzip entire sites, places this on a server in a city, and provides access with a self-signed cert that everyone involved with knows about.

Or failing that, some kind of digital dead drop with the files. If this could be updated a few times a week, that's better than not having access to material that you don't want the government to know about. It has to be possible.