What is your point? The icebergs, like the one that hit the Titanic calve on the western coast of Greenland and float south with the stream into the Atlantic. The Titanic was hit in the North Atlantic and the bergs continue to travel south into warmer waters where they are completely melted along the way. The Titanic berg was thought to have probably made it another couple hundred miles before being completely melted. Some very large bergs can travel into the area of Bermuda. Only about 12% of icebergs calved from Greenland make it to the North Atlantic although the actual numbers spotted per year varies.
The Gulf Stream begins in the upper water layers in the North Atlantic about in the area where the Titanic was struck. One stream heads North and the others do go clockwise to the south where the steams break out again into regional patterns that follow coast lines and link up with the streams from the south and begin their deeper water travel to the north along the coastal trenches.
My point is that the bergs are traveling away from the gulf, not toward it.
The Gulf Stream originates at Mexico’s southern border, and travels eastward and then northward out of the gulf.