Also, the Bering Strait was iced over, which meant a much larger volume of warm tropical water was rushing straight at Greenland and the north Atlantic.I'm sorry, I don't really follow that. The Bering Strait is between Alaska and Siberia which is a very long way from Greenland and the Atlantic Ocean. Also if it were iced over that would block flow from the south (the Pacific Ocean) to the Arctic Ocean not increase it.
But more than that, before the ice caps had fully melted there was no strait between Alaska and Siberia. It was land which would have fully blocked water from the Pacific to the Arctic Ocean. Even now there isn't much flow from the Arctic Ocean to Greenland from the North Pacific and it's anything but warm.
Link to article
Below is a graphic of the known full extent of the northern ices sheets.
My understanding is that oceans and ocean currents are the primary driver of Earth's average temperature.
When the Earth began to warm around 20,000 years ago, warm tropical water naturally began to move towards the poles.
Because the access to the North Pole was so constrained, much of the warm water generated in the Pacific and Indian Oceans bypassed Antarctica and turned northward into the South Atlantic.
On the flip side, larger volumes of cold water began flowing south from the north polar regions towards the South Atlantic.
This is why I said Greenland was an outlier for average temperature around 11,700 years ago.