>> (e.g. anything where the servers are not connected to the Internet and do not even have every-few-days Internet access
It is possible to add your own root certificate to clients on the LAN. so the equivalent of hand-distributed keys. Granted, this leads to unwelcome other problems (you can't limit your root to your local domain) so it's not often done, but it is possible.
Personally I prefer the DNS-challenge approach I described in a sibling comment.