I'm looking for advice setting up time servers for a very non-typical network. I support many closed networks that have occasional access to the internet. A network would get access most days for a few hours, but would frequently go 1-3 weeks blacked-out. The computers/servers on this network are mostly *nix-based, but not all the same flavor. The entire network is mobile, so when it connects, it will have very different hops/latency to internet time servers. The servers on the closed network are powered-off frequently (at least daily). Right now, my gut tells me to use NTP (because I hate re-learning all the stuff that someone else already got working pretty well). But I have several issues, and am looking for someone with experience in this type of strange situation. I currently have no solution in place, I'm simply letting the internal clocks drift. This results in errors of ~600s in a majority of networks. I have seen mismatch worse than 10,000s.

1. Is there something "better" than NTP in this situation? I know NTP likes to have very frequent, consistent access to servers that give nearly identical answers. I won't have that.
2. How many internal NTP servers should I configure, so that during periods of internet blackout, I have internal time that is consistent within the closed network?
3. There is no human access. No matter how large the mismatch, the server(s) must attempt to correct itself.
4. Discrete steps are very bad. No matter how large the mismatch, the correction must be "slewed", not "stepped". I understand that this could take many hours to correct.