I don't think a static Mastodon or Lemmy is very useful. For PeerTube that might be something to consider.
Providing a read-only, static version of the services, particularly toots and blog posts, while the origin is unreachable is straightforward and inexpensive.
Somewhat related, the Solar Protocol [0] does something like this to host websites across an array of solar-powered servers across the globe. http://solarprotocol.net/