Migrating state data from 1 Persistent Volume to another has gotten quite a bit of use. Originally created to help with the Legacy storage migration, the uses have multiplied as teams have more and more stateful applications.
Automation now exists to migrate stateful data within the same cluster, and a walkthrough for an approach to migrate data between clusters has been developed too (only waiting for community support to automate!)
Github project: BCDevOps/StorageMigration
Automation Migration Walkthrough: MigrationSteps
Cross Cluster Migration: CrossClusterDataSteps