Unlike pills I've always had very warm feeling towards herbs and I do enjoy preparing and taking them. And I have had tremendous benefits from doing so.
First, I want to stress out that what I am doing is experimental, so what follows is just an account of what I have been trying: no conclusions much less recommendations!
The purpose of this introductory part is to outline the picture about Hashimoto I have in my imagination.
As an assistance to this task I read the excellent resource  which I recommend for comprehensive details well presented.