According to the docs and from investigation Triton stores all important persistent state in the manatee cluster, which is a cluster of postgresql instances.
The manatee cluster itself depends upon the binder service operating which provides zookeeper and DNS services that manatee makes use of.
Most services store the state in manatee via Moray. Moray provides a key value store API that is backed by manatee. Restoring binder, manatee and moray is the main part of a restore. All other services depend on these services and are almost completely stateless.
Depending on how images are configured in the event a complete headnode loss images will not be restored as they are only stored locally.