Very interesting article. I always wondered what the level really was. I've wanted to try making NA beer, but the process is not so easy and you basically risk wrecking a 5g keg of beer you took 2 weeks or more to make. It's notoriously difficult to remove the alcohol without causing other changes, and doubly so as a home brewer where you don't have industrial controls.
I make my own BBQ sauce and it's a whiskey sauce, but that is reduced for hours on the stove, so likely it's at the minimum or near 0% when done, but obviously not 0. Still, it sounds like you are sensitive to something more than just the alcohol. Maybe something else present that comes along for the ride during the fermentation process. There's 100s of compounds that can be produced depending on how something is fermented. Different types of yeasts and bacteria have all sorts of by products. If you're still sensitive after nearly all alcohol is removed, maybe alcohol is just the common denominator that seems most obvious, but isn't really the problem (directly). Idk.