Yes that would make sense, too little might stop your stomach from producing its own HCL. I have not heard anyone stalk about the symptoms you get though and if i were you i would be worried about taking a big dose. If your up to experimenting though, go for it and take a handful.
Salt is supposed to help with acid production, as well and bitters and lemon juice. You could try a shot glass of those three before a meal.
Besides that i would just recommend a diet free of fiber and tough meat, very low in fat and high in easy to digest carbs and protein like dairy. Your TSH is steller but that does not paint the entire picture and you still have a ton of hypo symptoms, trying some cytomel might not be a bad idea. On and since your in Washington, smoke more weed! Supposed to help with digestion. Also raw milk is legal.