have no idea, never heard of that one

Joe was always trying to show his authority. He made many many false statements and claims (actually every one of his statements and claims were false). He was always trying to one better his previous claims. Every time Joe was doubted or assumed guilty of something, he miraculously had a new revelation to weasel out of the current predicament. Joe needed to show Mormon superiority. So why not make up a new revelation. Hay guess what guys (and subordinate female people) this is were Adam and Eve lived. Joe was lucky that way. He seemed to always be in the right place at the right time. Found a bunch of gold in New York. Just happened to have sex with other women and girls, under the strict instruction from his god. By chance happened to come across the scroll describing the life of Abraham. He was lucky that way.

Is there a Garden of Eden in Missouri?

Simply: because their founder, whom they believe to be a prophet, Joseph Smith, declared so.

Because Joseph Smith said it was. His pronouncements are accepted as "gospel" by the LDS Church.

Well, we know what site of biblical significance is in DC.

You are correct that Latter-day Saints tend to believe that the Garden of Eden was in or near Jackson County, Missouri. The Scriptures don’t actually say where the Garden of Eden was located, but they do talk about a place called Adam-ondi-Ahman, which the Lord revealed was Adam’s name for a location now known as Spring Hill in Daviess County, Missouri (Doctrine & Covenants 116, https://tinyurl.com/dc-116-01). Since Adam probably didn’t travel huge distances in his lifetime, this gives us a clue that the Garden of Eden was likely in that vicinity. * * ¶ * * Beyond this, several of the early Twelve Apostles of this dispensation (i.e. those called in the 1830s and ’40s) recorded that the Savior instructed Joseph Smith, Jr. (who then presided over the earthly Church of Jesus Christ) that the Garden of Eden was located in what is now Jackson County, Missouri. (There’s a good treatment of this at https://tinyurl.com/ensign-1994-01-16.) * * ¶ * * Unfortunately, Joseph Smith (who had only a second-grade education) didn’t have any scribes at the time, so there is no firsthand record of this revelation; but since multiple, reliable witnesses attest to the statement, it is generally assumed to be genuine. * * ¶ * * HTH! 😊