I don't really have any advice to offer. I just want to offer my sympathy. I am so sorry to hear that you are dealing with this issue. I, too, have been living a nightmare for over 5 years since I became super hypersensitive to mold. I was never bothered by mold at all until 5 1/2 years ago when my work relocated to a renovated building. Not only was I affected by the toxic chemicals from the redo (I have severe Multiple Chemical Sensitivities), but I began to realize later that the building also has mold (though I can't seem to convince the powers that be of that). Shortly after that I began to be affected by mold in the older house we lived in that had never bothered me before. And that just accelerated and got unbearable. I've lost numerous possessions and may lose more if I can ever get things out of storage. I may not have gotten some things out of the house in time. I finally had to bite the bullet and move. And discovered later that the place we moved into had mold as well. It's very hard to find a rental that I can afford that will not have mold to some extent. And I have become so sensitive to it that I react to minute amounts of it. I joke that I could have a new career as a mold sniffer. I react and smell or "taste" mold where no one can. It's in my office, my home, and my car.
I've tried every kind of air purifer you can name just about. I have an ozone machine going in my kitchen and living room area where no one spends any time much. I have 3 different kinds of machines going in my bedroom trying to have at least somewhat of a safe place to be. But I'm fighting a losing battle with that. I'm not just dealing with mold spores and such. The mycotoxins are not easy to deal with. The one kind of air purifer that I found to be halfway effective against just mold spores was an Airfree. It works by heat. But it does nothing for the odors that are put out by the other things to with mold. It's really minimally effective at least in my situation it was. I also found photocatalytic type air purifiers like Air Oasis to be more effective against mold than ozone ever was. But they also don't really handle mycotoxins. Ozone doesn't either completely though I have found it be better at handling the odors that emanate from it. It does keep it at bay somewhat. I have turned the machines off to clean them or to have them off a while if the landlord was coming in to do something. And after the ozone has cleared and some time has passed, I begin to smell the dirty dank smell of the mold and be more typically affected with burning eyes, throat, lungs, sinuses. So the ozone is helping somewhat. Some people can't tolerate ozone at all though. As far as using an industrial type ozonater, I doubt that just running one for 4 hours would do anything anyway. Plus, you probably still have a source of the mold somewhere that perhaps you can't see. Mold is a very insidous horrible thing to try to track down and eliminate.
I do wish you and your family well as you struggle with this and hope you find a solution.