Update: Okay, so after another round of testing with NS Support, what I discovered was that I was wrong (yay!) that it does update the way y'all are saying. However, it seems that updates to the template take multiple days (boo!) to make their way to the printing checks screen (at least in my sandbox account). We tested this a number of different times and cleared cache and used multiple browsers and confirmed it was indeed using the advanced template, but when changes were made to the advanced template they did not reflect in those printed checks at all. It was still showing the advanced template version that I had put in place a week ago, not the current version.