For me gluten is a problem and causes inflammation. You may have to figure out what causes inflammation in your body and eliminate those things.
Interestingly enough I spoke with an md who verified this very thing, anything causing inflammation in your body is going to be a culprit for auto-immune issues such as hashi. If you can keep the inflammatory response down you can keep the attack on whatever organ or system you are dealing with, well I think this goes for most issues within the body. Unfortunately we have so many things we are reacting to that it's like trying to find a needle in a haystack when we start eliminating and find at the end of this scenario, is there anything I can eat/use? Good question and I think one that has been a lengthy topic on cz for many issues. So for instance, you have a group of people that have hashi but for 10 of them they are gluten sensitive, then there are two others that seem to be intolerant to dairy...and so forth.
I think there are blood tests now that can detect what foods you are reacting to...if I remember right it costs about $450 or there abouts..you can request it from certain md's who lean to a more natural approach.
as a side note you will find that in many hashi/hypo people that gluten is a definite issue.