Both proteins and fats are converted into glucose during periods of fasting, starvation, low-carbohydrate diets, or intense exercise. This process is called gluconeogenesis.
If it is true and cortisol is essential for gluconeogenesis to occur, then sufficiently restricted carb intake (eating close to zero carbs), which requires more or less continuous gluconeogenesis in order to maintain blood sugar, may result in steadily elevated cortisol levels or high demand for cortisol. In this case adrenals are permanently stimulated.
On the other hand there are the high carb diets which, although do not induce gluconeogenesis, constantly burden the adrenals as they have to deal with the highs and lows of blood Sugar and keep it stable.
IMO, the ideal diet to recover from AF would be the one that provides JUST enough carbs to nearly eliminate gluconeogenesis.