Repairing did not work.  In fact, the repair failed on all three terminal servers due to some temp files being missing, so the repair had to be rolled back.  I ended up using the installer to perform a repair, but even after that, the same error persists when exporting to Excel.

We tested on another computer at another company running the same version of Quickbooks (Enterprise 18) and the same error persists there.  I have a feeling the problem lies with the pivot table template file (the .xlt file mentioned in the error) that QB installs.