Hi Jon, you can use Kibana's Saved Objects app to export and import Dashboards. Note that you will also need to export the Visualizations, Saved Searches, and Index Patterns used by these Dashboards. When automating this work, you can use Kibana's Import/Export Dashboard API.
You can use Elasticsearch's Snapshot and Restore APIs to create a snapshot of your .security-* and .security indices and restore them on the cluster you want to copy them to. This guide on the subject provides more detail. When working with snapshots and repositories manually, Kibana also offers a Snapshot Restore app to make the work easier.