Hi Steve,
No need to create a new set of banks. You just need to have all three question banks accessible from the course where you are placing your three quizzes. For quiz 1, edit the quiz and select, Add > random question. Then select the Category and number of question to add, then click, Add random question.
Repeat the above for quiz two to get random questions from the same category. Once you have the questions added from the first category, click on Add again, but switch the category to your second one, and tell it how many questions you want.
For quiz three, repeat all the above and then click, Add, a third time, and select your third question category and the number of questions.