People who advocate a Mesoamerican setting claim the Book of Mormon describes Mayan culture. I'll take a look at the comparison.
Here, I'll look at the 400 year claim. Some Mesoamericanists think that the term of 400 years mentioned in the Book of Mormon (Alma 45:10, Helaman 13: 5-9, Mormon 8:6, and Moroni 10:1) is evidence of Mayan culture. For example, in Mormon's Codex, Sorenson writes, "An intriguing possibility of a detailed Mesoamerican correspondence with the Book of Mormon arises in connection with the prophecy of Samuel. He had announced that "four hundred years pass not away save the sword of justice falleth upon this people" the Nephites (Helaman 13:5, 9). (Here he nearly echoes Alma in Alma 45:10...) Another cycle in the numeration of some [Mayan] groups was 400 years. The 400-year prophecies by Alma and Samuel would be on a potentially correct calendrical target, even though so far we lack documentation form secular sources that prophecies occurred for a like period."
That's the Mayan explanation.
Here's the Hebrew explanation:
Genesis 15:13 And he said unto Abram, Know of a surety that thy seed shall be a stranger in a land that is not theirs, and shall serve them; and they shall afflict them four hundred years;
14 And also that nation, whom they shall serve, will I judge: and afterward shall they come out with great substance.
There are several references in the Book of Mormon to the children of Israel being in bondage and being freed. I think it makes more sense for the Book of Mormon authors to look at the 400 year period in the context of Genesis than in the context of a Mayan culture they never mention.