I wouldn't have thought poop to be a good source for DNA, but then perhaps it does contain a lot of a human's enzymes and digestive juices. Saliva works, so why not from the other end...
I say we clone one of those guys to see what he looks like, and refer to THOSE people as "native Americans".
We already have at least two reconstructed skeletons, Kennewick Man (9,300 yo) and Spirit Cave Man. Spirit Cave Man is 9,400 years old and the oldest mummy ever discovered in the Americas, he looks suprisingly like Kennewick Man.
The internal lining of the human intestine is frequently shed and regrown.