An equitable solution to a problem at work regarding sick leave and staffing?

Please bear with me as I'm not terribly sure if this is the right place for this, if I'm phrasing it right, or if I'm making a mountain out of a mole hill.

I work at a childcare center - a private school marketed as "the best in the area". By most metrics, we are exactly that. I've worked here for nearly 15 years in a variety of roles, namely as a prek teacher for over half of that time. I have a good relationship with my directors and the schools owners, despite some issues in the past (I'm eager to champion more rights and privileges for employees).

This week was the sickest I have been in years, and it was the same for several other staffers as well. We couldn't call in, however, because none of us had fevers, vomiting, or diarrhea (the "big three" for what's acceptable to call in for). We all had flu-like symptoms, though those of us who went to the doctor tested negative for anything. Dozens of students had been getting ill with STREP, Influenza A/B, and Fifths in the weeks prior. It just took its time in reaching the staff!

I co-teach in my class and my co-teacher and I both lost our voices for days. Others had full-body aches, tremendous coughing fits, extreme lethargy... It was terrible. However, almost none of us got the time off that we needed to recover. Why? Staffing. The owners/directors don't want to close a room due to illness, even if both teachers in the room are horrendously sick. I spent days with the kids, barely able to talk or move, just trying to get through the day. My coworkers were the same.

Does that seem right?

The directors/owners essentially picked those who were deemed "sickest" to take a day off. While in the moment I understand that decision, it doesn't seem like a terribly good way to handle it either. I want to bring up my grievances about this with the owners (I already have with the directors, they don't disagree with me but "that's just the way it is") but I also know that showing up with a problem and no solution won't go over well. I also know they don't want to close a classroom at all costs, which is my preferred solution. The last time one was closed was when 5/6 teachers in another room had COVID simultaneously and we were mandated to close the room.

Anyone have any thoughts? Even if it's to show me a side I may not be considering here? Thank you for your insight.