I've since spoken with Nintex Support and was advised that it is best to contact Nintex when upgrading 5 or more versions. An upgrade path can be provided and intermediary Nintex trial versions can be provided for use to make a stepped upgrade.
Our ULS logs began showing hundreds of "The input data is not a complete block. (Build:3180)" and "Padding is invalid and cannot be removed. (Build:3180)" appearing in the Nintex Workflow 2013 area of the logs. Additionally we found that an action which uses an impersonation accounts credentials to execute was failing and had to be removed and re-added to the workflow. One site (out of more than 30) began logging 'Error in task. Cannot find a corresponding human workflow task id for this task.' The PowerShell script used for creating our HNSC and adding workflows began failing to get a the Nintex Workflow Service proxy. Workflows appeared to be successfully added but could not be seen in the redesigned workflow gallery.
We are working with our provider and with Nintex Support on troubleshooting and resolving these issues. Hopefully we will not find ourselves making this kind of leap in the future.