With posts like this, I wonder about the REAL REASON behind asking the question. No doubt, headaches can be caused by MANY things, but considering that essentially ALL MUSIC, depending on perspective is out of tune (mean tuning, well tempered, just tuning, various historic tuning schemes etc.), I wonder if the problem is not self generated, if ones tolerance (having to teach a big group) simply is the problem.
I don't think that the instrument being played nor the quantity is critical. I think that stress is a function of attitude and has deeper roots.
As far as instruments not holding tune, that is certainly something that can be fixed - one instrument at a time.
If we do not have what it takes to teach big classes, then don't. I believe that teachers are born, not "taught".
Chemicals are certainly a workaround and not a solution.
I bet that there is much more to the story. My hunch is that to stay employed, taking the large group was delegated regardless of the teachers opinion or excuses why not.