I am not sure if I completely understand the scenario, but I will offer my thoughts.

In round one, since the instructor knows exactly which questions she wants in each of the three quizzes, I would create three separate quiz question banks with these specific questions.   I would probably first create the category, then I would move the specific questions into each of the three categories.  Moving questions into a new category is pretty simple.

Then, I would create one more category (maybe named Quizzes 1-3).  I would export the questions from the first three categories, then import them into this one category.  I would then end up with one category with the questions from quizzes 1 to 3.

By the way, since in the first step I had to "move" the questions, while I was at it, I would import the questions back into each of the original question categories.

Hope this helps.