An interesting case, and I'm sure more teachers / course designers would like something like this to work in Moodle. Currently, the only way to set this up is through separate quizzes that pull random questions from the question bank's categories. These quizzes could be linked through Restrict access so all subsequent quizzes only come available after the previous one(s) have been completed.
You could use the gradebook setup to properly display the final grade for all quizzes in the gradebook category, while hiding the grades for each individual quiz.
The alternative would be looking at the Lesson module, but that has very limited quizzing possibilities.