I'm dealing with the same thing and have maybe done close to 100 fasts, some as long as 3 weeks.
I still have hashi's but it's way better. The brain fog is starting to vanish. I can really tell when the antibodies flare up.
I believe the problem is adrenal. Stress causes adrenal fatigue. Everything is so stressful nowadays, and that takes a toll on the adrenal glands. This is what I personally believe causes the antibodies and therefore the problems with the thyroid.
So fasting is helpful but also getting rid of as much stress as possible.