There are at least two ways that glutathione can interact with methylation capacity:
1) Glutathione appears to be required in order to import B12 into the cell, so cells that are low in glutathione may have a hard time utilizing B12. Boosting glutathione in these cells should increase the cell's methylation capacity.
2) Furthermore, a reduced methylation capacity theoretically slows the production of glutathione, so a reduced methylation capacity may worsen low glutathione levels. So cells with a low methylation capacity could develop low glutathione levels.
It is very common to have strong, unpleasant start-up effects when boosting methylation capacity or when taking NAC. Rest assured that these may just be temporary start-up effects, not "overmethylation". Indeed, I can not find any scientific concept of "overmethylation". From what I can tell, people might have invented the term "overmethylation" to describe the strong, unpleasant start-up effects.
Hope this helps.