Without those currents the icebergs breaking out of the sea ice wouldn't have gotten much momentum ~ making travel in a small boat relatively safe even in mid-ocean. I would imagine this would even have a serious impact on hurricanes and that would have extended the sailing time into the warmer months giving the Sa'ami plenty of time to reach America.
I think we can come up with a specific date for when the first Europeans could have arrived in America via an Atlantic route now.
They could have walked across the ice.