It does interact and have side effects. Any kind of amino acid chelate should work just fine. Zinc monomethionate looks promising. I don't think it is any better than any other form. In fact, maybe a lot more.
Copper is very interesting.
If you look at how many copper compounds have been synthesized and looked at as analgesics and anti-inflammatories, it is astounding. It is thousands. There have been some that have been used injectably in Europe with amazing results. If you use copper salicylate you have an even better aspirin. You can get to a copper toxicity, which is one limiting factor for these things, so if people feel better they'll take too much for too long and they may end up with too much copper.