'Elephants' in America?

One of the more outlandish claims of the Book of Ether is that there were elephants in the promised land. While we know that wooly mammoths and similar animals lived in the Northern Hemisphere during the last Ice Age, the question is how long they survived before becoming extinct. If there were remnant mammoth populations in the Americas during Jaredite times, this could be a good explanation for the 'elephants' mentioned in Ether 9:19.

Surprisingly, small populations of mammoths survived until relatively modern times. It is now accepted that a group of mammoths were still living on a remote Russian island in 1650 BC. This is pretty much what we understand to be at the start of the Jaredite time period as depicted in the Book of Mormon. Could there have been other groups still on the American mainland, and perhaps even as far south as Central America at that time? This is a controversial suggestion, but various explorers in the Americas have described seeing what could only be understood as mammoths, even as recently as the 19th century. Some of their accounts are reproduced in this video.