I haven't read Kon-Tiki, but I did read The Brendan Voyage. Actually inspired by Kon-Tiki, I think, a group decided to build and sail a reed boat from Ireland to North America. There is a story, long considered a legend, that Saint Brendan and some monks actually did this. The story has a lot of elements that seem to resemble real things they might have encountered, so it seemed like a worthwhile effort.
Also an interesting read.