Post Duplicator + Pods

We are using the plugin Pods to build a number of custom content types and then to display them. Specifically, we are creating a database of nineteenth-century print trade journals. As we enter journal issues, the information is often similar and so it would be useful to use Post Duplicator to duplicate all the information and then go in and change the small bits that differ.

At the moment, Post Duplicator can replicate all of the plain text fields in the Issue pod, but it fails to duplicate fields that pull in content from other pods (i.e., other data tables).

Is there a way to use Post Duplicator to duplicate all of the content in a Pods-created post?