Yes, zinc is THE copper antagonist. You can also use N-acetyl cysteine, but this also removes some zinc. If you supplement zinc, go very easy on dosing, as all your symptoms will worsen when copper is released into the blood. It was my anxiety and racing mind which led me to the copper theory. These two symptoms especially worsen during zinc therapy. It is important that you stay away from high copper food such as all nuts, advocado, raisins, prunes, dates, curry, black pepper, tap water, beer, tea and iced tea, whole grains, chocolate, mushrooms, shellfish, organ meats such as liver, multi-vitamins with copper, soy and seeds (except for pumpkin which have a high zinc content). Birth control pill will increase copper accumilation. Alpha lipoic acid blocks copper from being excreted in bile, so stay away from this popular mercury mobilizer.
Then it's important to limit food which lower zink levels such as sugar, grains, refined carbs, alcohol, coffee and fiber.
Lastly milk products should be avoided because of calcium. This mineral slows metabolism and this contributes to copper accumulation.
Best foods to combat copper toxicity are vegetables combined with all kinds of meat. Small amount of fruit and limited amount of refined grains. Also include small amounts of good oils. Eggs and pumpkin seeds. Garlic and onions for sulphur. Cinnamon and ginger.
Managenese, iron and molybdenum also chelate copper, but then your body might react badly if you have mercury toxicity in additon....your body might then not be able to cope well with the above metals. I had to stop chelating with these and now only use zink, diet and sulphur. Again, go slow on zinc supplementation. After much trial and error I found the best way to deal with a copper problem is to take a small dose (in my case 5 mg) every three hours throughout the day rather than three capsules which gave me ALOT of trouble and discomfort. Also if you have high aluminium...like me....zinc is this metals antagonist also so it's important to stay away from deodorants and anything cooked or wrapped in aluminium foil, antacids, cheese, aluminium pots and pans. Anyway, best of luck!
Hope this helps some ; )