This is a super interesting read! In my previous conversations with Prof. Fehren-Schmitz he was highly skeptical of any Pre-Columbian contact based on his findings in [1]. He says the issue is pretty strongly politicized, because there's a modern Polynesian immigrant community in Peru that would "benefit" if admixture is found, while the Polynesians in Polynesia are a lot more skeptical due to nationalist tendencies. I might be getting this backward, not completely sure, but his point was basically that it's super hard to study this specific issue because of the surprising amount of politicization there is surrounding it.

[1] https://www.cell.com/current-biology/pdfExtended/S0960-9822(...