Here are my numbers before and after:
In addition to going gluten-free and (mostly) dairy-free, I also have stopped drinking coffee, started taking 1000 IU of Vitamin D3, and have been taking a smaller dose of T4. I have also backed down a bit on my workouts and have been trying to get more sleep.
The most important changes are the decrease in CRP (an inflammation marker) and in my thyroid antibodies. The changes to my thyroid hormones are probably mostly due to the dose change.
I had noticed almost immediately that I had less aches and pains after dropping the gluten, even after a tough workout. I might have muscles that felt sore, but my joints didn't hurt.
I think that this is a big change in such a short time. I am hoping that if I continue to make healthy changes, I can see these numbers get even better.