I only understand a little and could never guess what the DoL would actually determine.
From what you said, I could see where the instructing was 1099 and the coordination was W-2, but you mentioned it was the opposite. Double check that. Specifically because the coordination efforts seem like they would tick all the boxes for employee.
If the company dictates the how, when and where of the classes, it seems more like an employee. If they facilitate that and it’s more you can teach your class at our facility and here are the open times, that seems solid gray area.