Good luck with that! I know it's tough--old habits die hard. But, you're right: It looks like endocrinologists are suggesting that Hashimoto's patients lay off the sugar substitutes, especially aspartame.
Here's one article I found. The arthritis foundation website suggests the same for inflammatory arthritis, but their website is getting too pop culture for me to value it much.
There are lots of different sugars used in our foods, toothpaste, mouthwash, etc.
Here's a list I found from the Mayo clinic. A varied diet is important. Lots of "natural" things are not meant to be consumed in large quantities. That Splenda makes me nervous because it's so stable....and stevia is natural, but looks like a scary molecule to me.
Giving up artificial sweeteners won't help everyone. Won't help me with autoimmune disorders, because I never consumed them in the first place. That genetics component is too strong.
...hope it works for you...