"Why did I seem not to make progress for months when I was using 100mg ALA and 50mg DMSA without stop? Why did I feel so much worse for so long when I stopped, if I'd pulled mercury out? "

Perhaps your body reached an equilibrium state, and the mercury remaining was very tightly bound. With time the body naturally detoxes, so some of the tightly bound mercury moved to a part of your body where it is not so tightly bound, so now it can be removed.

The Lugol's solution is a good idea. I suggest that you add zinc and selenium to your regimen though, as many mercury toxic people are deficient in these, and selenium doesn't just help get rid of mercury, but is also so crucial to convert T4 to T3. Zinc is important for the immune system.
Vitamin c and b vitamins are good, but don't go crazy with them. I take 2 grams a day of vitamin c. Some here take over 10 grams a day. Magnesium is also very important.