while everything you said makes sense, the thing I keep coming back to over and over again is that the oldest human remains in the Americas have always been in South America. Which to me has always implied that the first people arrived in South America from somewhere, and the closest possible racial match is the Polynesians.
If anything, since the population of South America is many thousands of years older than anything in Polynesia, it means that Polynesia was colonized from South America. :^)