What do you think of my idea? That the Moodle Quiz module should stagger the quiz starts automatically. Perhaps an AJAX response like "Please wait in queue, server is rending quizzes for 3 students..."
I've seen multiple posts where Tim Hunt mentions that teachers should "yell" at their children to not start the quiz at the same time. "Think of the server!!"
Here's a post of Tim's that approves the idea of simply making a long password for the quiz. It will take everyone a different amount of time to type in the password which prevents everyone from pressing the button at the same time.