I don't think I have ever paid a corkage fee. What I do is try to get to know the manager of the restaurant. Maybe dine there once before and meet him or her. Then, I would tell them I want to host a big dinner at their restaurant, which they are usually quite happy to hear. And then I say, "if you don't mind, I would like to bring a special wine that my guests have requested." Works for me.
One other point, there are hundreds of nice restaurants in NYC. You can call the manager and say that you think this fee is too high and if they refuse you, cancel the reservation and go somewhere else. In any negotiation you have to be prepared to walk away.