UPDATE: May 2017: There is a solution that is available to higher education institutions (only) and it is called Device-Based Activation (DBA). I am calling on Microsoft to address the issue with a real fix. I am proposing two workarounds that could help and one I’ve included just for completeness. This blog post details the common licensing and deployment practices for higher education labs and the particular conundrum it causes with Office 2016 and Visio/Project 2016.
While the particular scenario I am describing here is likely common only at educational institutions, for those affected, it is a major showstopper.