I chose PMroz' method as 'correct answer' because I felt creating a subset using only the required columns was slightly more concise than duplicating the table first and then deleting columns, but obviously the other approaches work equally as well.
This solution does the trick for me. I am still surprised though that there is no option in the Update command to just add one particular column and leave everything else in the target table untouched. I initially thought the "Add Columns from Update table - Selected" option would do this, but clearly this is not the case.
Thanks again for all your replies, I really appreciate it!