At best the BOM is a clever mixing of several traditions and histories. Even a devout Mormon like Thomas Ferguson could find nothing, and he has not been alone in that, both archaeologically or in Genetic Science.
The DNA evidence is equally as thin, the idea of various human migrations to the new world is a continuing field of study, but any DNA links can be explained my simple migrations, and do not provide equal evidence of a massive civilization that should have numerous ruins and mentions in the oral histories of the Native American people.
Grasping at other cultures as proof is tacky, but expected. You should have snagged the Incans or Mayans, their ruins still stand, and you could lay claim to their "ancestors", the 12 Colonies of man from Battlestar Galactica. After all it is a modern fairy tale as well...
Moreover, if you know anything about the people in the Book of Mormon, the descendants of those inhabitants are referred to as the Lamanites. In the Doctrine and Covenants, Joseph Smith called several bretheren to take the Gospel to the Lamanites, as had been promised them in the scriptures. Every tribe he sent missionaries to is a member of HaplogroupX. That is not coincidence. You might also take note, based on your previous assumptions as to where the Church or the Prophet thought the Lamanites lived, that he never sent anyone to preach to the "Lamanites in Central America" He does not even mention Central and South America. For years anti Mormons have propped up academics who are also members of the Church and their belief that Central America was the setting for the Book of Mormon. The only fruit of their quest to make it so has been to divorce themselves from the Prophet Joseph.
He never said anything about Central America, which has been more of Church culture, since no Prophet of the Restoration has said that is where it was. In fact, as late as 2 years ago, the late Gordon B. Hinckley (Prophet of the Lord's Church) said the evidence had not come forth yet. It was in a discussion with a German reporter who thought to score some points when, at that time, DNA evidence showed no link between the indigenous lines of Central and South America with the Near East. All of the Church critics were quick to seize on this as a "nail in the coffin" to Mormonism. Little did they know that just two years later a confirming witness would come forth, not just showing a "European" DNA haplogroup- in which researchers would include the Near East, but strikingly confirming its link to Israel specifically, which is where the Book of Mormon says they came from.
I will continue when you have done more research. I won't spoon feed you the rest. Let me know if you have any questions on what you find.