It does not even appear that the Titanic ever crossed the Gulf Steam. It appears that she crossed much cooler North Atlantic Current. I've read that a passenger on Carpathia moved his chair to shade at 5 p.m. Sunday night. They did cross the Gulf Stream. BTW does somebody know how much south of the wreck site the Carpathia was at 5 p.m.As you said, its ever changing. The attached shows the situation in April 2016. The overlay shows the track taken by Titanic in 1912.
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The following shows the situation 10 years earlier in April 2006.
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I have a record of this from 2003 onward. These are satellite radar images showing the velocity vectors of the ocean currents.