The Istari arrived in Middle-earth after the first shadow had fallen on Greenwood. Why do you insist, Barahir, that Gandalf's staff was made from the wood of this forest? I just can't think of any source which suggests this.
I think it likely that the Istari brought staffs with them over the Sea; after all, they were in the bodies of old men and needed walking sticks. There's a thread near the top of the N & N forum about wizards and staffs. It's interesting.
Edit: It is called The True Istari. I'd link but I'm not sure there's such a thing as 82nd time lucky. ;-)