We would advise that you move your students only before or after the contest. The reason for this is that it will affect their performance in the contest.
If a students has started on the contest moving them to another class will reset their contest scores, it might also prevent them from answering further question in the contest. The reason for this is to prevent cheating by moving stronger students into a class.
The same applies to moving weaker students out of a class.
It is because if this that we advise that all classes be set-up before the students start playing in the contest.