If you listen to NYC traffic reports on AM radio(1010 WINS)where this bridge is mentioned almost daily its pronounced "Koz Cuse Ko." I have never heard anybody use the pronunciation you are referring to.
Growing up near Middle Village, I only heard “koz-e-oos-ko” or “koz-e-us-ko”. Have lived in Brooklyn & Manhattan ever since, and the same there. Definitely don’t listen to the radio. Can you find any clips where they say it this way on NY1... literally have never heard it that way.