This is old news. We've known since 1830 that a man named Nephi built a boat, and his father Lehi was given a golden compass ball called the Liahona that directed them from the Arabian Peninsula to South America where they built a massive civilization. After 400-500 years a curious man named Hagoth built another boat and settled Polynesia. It's all documented in the historical tome called the Book of Mormon. [Source: Former Mormon :)]
Your comment absolutely made my day! I just thought I'd point out that the specific geographic locations you mentioned are technically not official doctrine but are personal beliefs held by definitely many members. [Source: Current Mormon who prescribes to alternative theories]