For those who are not familiar with the different forms of mercury (Hg) that humans are most often exposed to I suggest that you read the following.
Pay attention to the points about the movement of Hg across the blood-brain-barrier at a medically useful rate in the second half of this long post. http://onibasu.com/archives/am/1594.html
Humans, unlike fish, convert methyl Hg from seafood consumption to inorganic Hg.
If the conversion takes place in the brain the resulting inorganic Hg essentially gets stuck there for a long time--20 yrs, maybe more.
My understanding of Andy's position is that the body already contains plenty of cysteine. If methyl B12 was able to methylate a *significant* amount of Hg so it could escape the brain, so many people would not be suffering from the buildup of Hg in the brain.
Andy indicates that maybe 40% of Hg toxic folks actually are sensitive to cysteine and other high thiol foods and supplements! They tend to feel better and can tolerate more ALA when they avoid foods containing large amounts of highly reactive thiol groups.
If you want to speed up the detox process, take doses every 2 hours, take DMPS along with ALA, try to do somewhat longer rounds, take advantage of and support the excretory pathways--bile flow, kidneys, sweat--don't skimp on antioxidants!
I suggest that you also post the question in the large Cutler support group at Facebook.