Experimenting without know actual levels may not be the best idea. Not to pop your balloon but how do you know you have toxic copper levels? Is this something you read about or do you have actual data to support this.
Copper is a very necessary element and is critical for many bodily functions, levels could be normal, high or low. Low levels of copper can be just as problematic as high levels.
Doing a TMA (and do yourself a favor and do the Trace Elements test) will help evaluate ALL mineral levels. It is quite important to tailor a specific plan based on your specific profile. Playing around with supplementation is not always a good idea.
Personally I think that NAC is overrated - I do better on using straight cysteine.
Methylation is very critical for overall body functioning and is a complex cycle that utilizes many nutrients. Typical deficiencies of B12 and folic acid appear as do poor cysteine levels. But other nutrients are involved in this such as choline, B2, B6, zinc, methionine and taurine - and there may be other nutrients also involved that I missed. For example, if B12 or folic acid are missing then toxic homocysteine levels will appear. If you have the resources, I would have some testing done to ensure you are on the right path such as having B12/Folic acid serum levels and homocysteine levels. I am sure some of the popular labs such as Metametrix have more extensive testing that could be done.