The other thing that museum samples indicate is that, prior to extensive European travels in the Pacific, there was another, genetically distinct form of the sweet potato present in Eastern Polynesia. And that appears to have originated from the southern population, focused in the Andes. It was already present in Polynesia before colonists left this region to settle in Hawaii and New Zealand.
Given that we already know Polynesians had the technology to engage in long-distance voyages across the Pacific, the simplest explanation for this is that they did make it to South America, probably somewhere around the year 1000. And, most strikingly, some of them apparently turned around and traveled back halfway across the Pacific.