Just found out that FUCHS oil company has released more than one grade of zinc free oil. I originally thought the GT1 was only available as a 0w30, which I thought may be to low a viscosity for a lot of users. But they have released different grades...
There is one oil I know of that claims to have no zinc.
It is made by a German caompany and is available all around the world. The company is called FUCHS, the oil is GT1. http://www.fuchs-oil.com/index.php/titan1/1/