Clearly, you know more about this subject than I do.
However...
The total change in average temperature in the last glacial was 11 degrees, not 18 degrees.
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.
Below is a graphic of the known full extent of the northern ices sheets.
