Unfortunately at this time, there is no way to do this. The act of making Persistent Redis requires the Container to be shut down and reconfigured to make use of a disk for its Persistent Storage. During this process the data is cleared. However, once the Redis Instance is set to persist this will no longer happen when Redis is shutdown/moved as it will dump its data to disk before shutting down and intermittently during runtime.
Find out more about Persistent Redis.