I spent 2 weeks in the American south last month, and I had a terrible time too. Travel has historically been very much about eating for me, and having to manage frustration and anxiety every time we to went to eat was exhausting and depressing.
+1 for fancier restaurants. It's not a practical solution for everyday, but if you can save up for a pricier place every few days, chances are they will be much more knowledgable and patient around your needs. Especially so over the phone if you call ahead to inquire.
We kept safe meat, cheese and crackers for lunch times on the road and we got by ok. It was far from ideal, but at least it took away the frustration around mealtimes and let me enjoy the non-eating parts of the trip.
Consider also looking for menus/menu items with dead-simple ingredient lists, essentially facilitating a whole foods diet. My one success with southern bbq was plain smoked chicken on a baked potato. Certainly was at risk for cc, but given the base ingredients, they would have had to go out of their way to put it near gluten-free ingredients. That was a memorably safe meal.
Also, you might post a thread about an upcoming destination city on this forum. I did that for a few spots near the end of my trip and folks were most helpful with suggestions of places they visited.