The otc vitamins are not high dose. It is true when you go very high, on zinc the copper ratio will change. There is a condition called Pyroluria, which requires really high dosing of zinc and B6 (since these are complexed in the blood by kryptopyrroles that are left over from a genetic error in heme metabolism in the liver). Those patients should be monitored by a doctor when doing that treatment over time.

This is the one I use. It has a small amount of copper in it, to balance the zinc:
http://www.iherb.com/Source-Naturals...lets/1361?at=0
This is a quality product and not expensive at all.
If it really bothers you...you can try one every other day. But zinc is really critical for preventing infections and protecting the skin.

I take lisinopril for my blood pressure, and it depletes zinc.
I take the OptiZinc at night, because some studies show zinc is better absorbed then. (why, I don't know, but it is reported in some papers). This is not a high dose. The treatment for bed sores in bedridden patients is 220mg 3 times a day for comparison. I believe the PolyGrip thing is inflated. I saw one report from U of Mich stating that the zinc found in the small number of patients might be due to a genetic error in handling the mineral. Much like hemochromatosis is for iron.