Mongols did cross the Bering Strait, but I believe, at a much later time than the Polynesian crossing. You're right.....it doesn't seem reasonable that they would skip NA. The other possibility is that a major catastrophe wiped NA clean.
Back in middle 1940s Dr. Frank C. Hibben, Prof. of Archeology at the University of New Mexico mounted an expedition to Alaska to look for human remains. The remains he found were not human, but what he found was anything but evidence of gradualism or uniformitarianism. Instead he found miles of muck filled with the remains of mammoth, mastodon, several kinds of bison, horses, wolves, bears and lions. Just north of Fairbanks, Hibbens and his associates watched as bulldozers pushed the half-melted muck into sluice boxes for the extraction of gold. Animal tusks and bones rolled up in front of the blades "like shavings before a giant plane". The carcasses were found in all attitudes of death, most of them "pulled apart by some unexplainable prehistoric catastrophic disturbance" (Hibben, 1946).