Clearly he needs a punishment that costs the students a lot of time. Maybe submit a 12 hour video of you doing every single problem in all the problem sets
This is actually brilliant. Quizzes are ideally used to get people putting in the effort: studying during the semester and nudge them away from procrastinating/crunching at the end (thus are low stakes). But even with low stakes they nudge people to cheat. It was technically hard previously to verify the effort directly, so a quiz result is a noisy proxy. But with current tech you could just record the effort itself. If you are going to do problem sets, no extra effort in recording it.