Hi! Welcome to 3FC!
I do not have Hashimoto's or Hypothyroid issues but I remember reading a few timse where a low carb, paleo, GF (gluten-free) and/or some sort of low inflammation type of diet is better.
I think this question would be better served in the "Dieting for Obstacles" forum since I've seen a few similar posts there, here is one
with a bit more feedback.