(GA) I'm a salaried employee and I think I'm incorrectly claimed as FMLA exempt and don't receive overtime despite working a ton of overtime hours. What should I do?

Location: Georgia, US

i work for a non profit private school/church as the director of media. I oversee and maintain all audio, video and lighting systems (AVL), schedule and staff AVL techs for requested events and teach students and volunteers AVL principles. I oversee a pool of volunteer labor and I have 1 teacher who is a direct report to me only in matters pertaining to operating AVL systems. I don't have the ability to hire, nor do I handle any budget. I have to request funds to install new gear.

My role is hybrid between both organizations and I receive 2 paychecks. The organization is 2 entities under one roof. I have an annual contract with the school but an indefinite one with the church. My benefits come from the school. My contract states that I am to work a minimum of 40 hours a week and it is expected in busy seasons that I work more than that. The rule is is that all systems must be ready to go by the following Sunday for church services and Wednesday for school chapel services. I am required to stay until the work is completed regardless of hours or time.

Currently the way it works is a word of mouth arrangement where if I work extra hours in a week, I work less the following week to compensate, additionally I technically have summer off from the school, however I am expected to use the summer to maintain gear and install new systems. This has worked so far, but there are times when I am unable to take less time the following week and so I am stuck with extra hours worked an no overtime pay.

Based off what I understand about FMLA status I should not be claimed as exempt, but I am. I have been told multiple times that "we don't pay overtime" which, again, based off what I understand isn't an option, but a legal requirement if I work overtime.

What I'm wondering is, am I correct in that my classification is incorrect? and if so, how should I go about making them change it? At the end of the day I'm willing to be flexible with my schedule as that's what the role calls for, but I want to make sure that my legal status is correct in case the situation comes up where I'm required to overtime without the ability to compensate with extra days off, which during the school year is likely.