@cneville1 You are facing a tough problem here. I don't know anything about your particular air purifiers, but I know a bit about how school districts handle contracts.

They typically want a bid for the least expensive one-size-fits-all solution, without regard to what is appropriate in each room. Then filters are installed without regard for proper ventilation/fresh air exchange or moisture management. The needs in a wrestling room are vastly different than a classroom or office. Staff receives minimal training, and there is no provision for ongoing maintenance, sometimes not even for a budget and schedule for replacement filters.
All of these factors are a recipe for exactly what you describe. My daughter, a high school nurse, describes wrestling rooms, weight rooms and locker rooms as germ pits, so close body contact and confined spaces contribute to the problem.
You need a thorough inspection by an environmental health specialist. District admin is unlikely to listen to you alone, but if you are accompanied by unhappy parents you might get action.
Have you approached administration with this concern?