I think you've been misinformed about adaptogenic herbs lowering cortisol. I have low cortisol and take ashwaganda and it helps me immensely. It acts very similar to testosterone in the body.
"but I've read that AF folks need to be cautious about low-carb diets...." Also seems like misinformation to me. A typical adrenal fatigue diet is low carb (especially Sugar foods), high protein and fat. I'm not saying that's the best route for everyone, but that is the typical diet suggested (and also what I personally feel best on.). On the other hand, some people on this forum do better with grains. You're gonna have to experiment with this. But, if you are doing low carb (no grains), definitely make sure to do high protein and high fat.