This is a VERY helpful post Dan!  Somehow, when going from GP 2013 SP1 to GP 2016 R2, we applied the interim update (2013R2) and in one of the companies, it did not create any of the tables on your "new table list".  So, I kept getting errors when it would try to access those tables to upgrade to Gp2016R2.  So, what I did was go to one of the other database and scripted out the tables and it worked.   We don't use those tables yet, so it was fine to go ahead and script out a blank table.. :)