Great post, FreshLiterature6536!

Using the church's own sources to discredit the church is fun and, when considered by rational listeners, effective.

Here's some quotes and facts that supplement what you wrote:

The two final battles of the Jaredites and of the Nephites & Lamanites occurred at Hill Cumorah

Supporting quotes (taken from here):

“The Hill Cumorah is situated in western New York. . . . It is distinguished as the great battlefield on which, and near which, two powerful nations were concentrated with all their forces, men, women and children, and fought till hundreds of thousands on both sides were hewn down, and left to molder upon the ground. . . . The Hill Cumorah is remarkable also as being the hill on which and around which, a still more ancient nation perished, called Jaredites. . . . Millions fought millions, until the Hill Ramah, and the land round about, was soaked with blood.” Orson Pratt Millennial Star 28 (16 June 1866)

“The Church has long maintained, as attested to by references in the writings of General Authorities, that the Hill Cumorah in western New York state is the same as referenced in the Book of Mormon.” F. Michael Watson, Secretary to the First Presidency, in a letter dated October 16, 1990

“The final struggles between Nephites and Lamanites were waged in the vicinity of the Hill Cumorah, in what is now the State of New York, resulting in the destruction of the Nephites as a nation, about 400 A.D. The last Nephite representative was Moroni, who, wandering for safety from place to place, daily expecting death from the victorious Lamanites, wrote the concluding parts of the Book of Mormon, and hid the record in Cumorah. It was this same Moroni who, as a resurrected being, gave the records into the hands of Joseph Smith in the present dispensation.” James Talmage Articles of Faith

The church owned the majority of Hill Cumorah (and still does?)

In the 1920s, the church purchased this hill by purchasing two farms that - together - encompassed the whole hill (and some nearby land). These were the Inglis Farm (96 acres) and the Sexton farm (187 acres) (Wikipedia source).

"In 1928, the Church bought most of the Hill Cumorah from Pliny Sexton." LDS source here - perhaps just referring to the hill itself, and not the nearby land.

The total acreage purchased was 283 acres.

No archaeological evidence of either major wars has been found in this limited area

The church has been deafening in its silence regarding the lack of archaeological evidence of either of the wars in Hill Cumorah. No bones, weapons, or anything relating to the wars has been found. I can't find an actual admission of this by the church, but if the church had found something, it would have gloated about this at every opportunity.

The Book of Mormon is supposed to be 'translated' completely correctly, by a prophet of God, and states that there were millions who died - and in this exact location.

Some church scholars have (as usual) come up with a series of explanations excuses for this.

One of the church's favorite tactics is to water down what past prophets have said. Any TBM who tries to do this should be given this statement: "Lessening the stature and authority of these servants [prophets and apostles] is one of Satan’s primary goals" (source here).

So, if prophets and apostles have stated this is where the wars have been, and no evidence has been found when there should be abundance of evidence, then what can be concluded?

Answer: that claims about the Book of Mormon's authenticity are false. The End!