How do I get the name of the workset each Revit link is placed on?

Is it possible to get the name of the workset each linked Revit model is placed on?

I have been running the Revit Database Export task with the Workset Data Option setting set to Exhaustive (and Medium), but my report options do not include a Workset Name or Workset ID for Revit link instances.  I also do not see workset information in the SQL database for the project in the RVTLinks tables.

I have project with over 200 Revit models, it would be very helpful if I could know if all their links were on an appropriate workset.

Thanks.