You sound just like me! My joints felt almost immediately better on reducing my thyroxine but unfortunately my other symptoms returned. It didn't matter which brand I took.
I switched to natural dessicated pig thyroid and found that I didn't get the joint pain and generally felt better. Unfortunately to get rid of my hypo symptoms completely I needed to increase to a point where I was getting my 'too much T4' joint pain again. I have had to reduce my NDT slightly and add in some liothyronine. The joint pain has reduced again. I still have some joint pain and suspect I have something else going on there. I was also tested for RA and lupus but was told that just because it is negative doesn't mean I don't have either. They will test again periodically. Some people with autoimmune thyroid disease tend to be prone to other autoimmune diseases such as pernicious anaemia and RA, to name but two.
There is evidence that show that a build up of T4 can cause pseudo-gout. The crystals are different from gout crystals and can be caused by too little T4 or too much for the body to handle. If the joint pain is relieved by reducing your T4, this could be the problem. I can't find the paper at the moment but will keep trying.
The bottom line is that you might be better with an alternative thyroid hormone replacement therapy such as liothyronine, liothyronine/thyroxine combination or Armour. You may have a battle on your hands getting this treatment though as many doctors don't believe they are necessary (they are also much more expensive than the £1 a month that thyroxine costs!)
I hope that helps