@bbennett2 -
Well I wrote all the stuff below and more or less decided I confused my self. I am sure that you can manipulate the information around, and it may very well depend on whether it is classic or new quizzes. If any of the stuff below makes sense, you can try it out. Might be a good idea to create a dummy course and try the various techniques in it until you figure out the exact procedure. I am sure it can be done, you just have to figure out what needs to be changed.
Ron
Random Rambling thoughts:
Based on the information you gave, they are using the copy function? Or are they doing an actual import?
As you know, Canvas assigns an id to any assignment for a course, so it does not matter if you change the name or not that number remains the same. So Canvas must be creating a link between the original and the copied quiz.
One thing you could try is in the master course, creating a copy of the quiz in that course. That will give it a new number. . you could then iimport that new quiz. However, I just realized that it is probably the question banks being overwritten themselves. You could try renaming the question banks in the course being copied into and then importing the copied quiz - or just the question banks themselves.