That's a quotation I have not seen before and I can't find, so I'd very much like the citation. I haven't seen one by Joseph that refers to Central America, or that refers to "all of the Americas" or to them being the promised land. If anyone knows of a quotation about these three items, please advise.
The preliminary question is how this pertains to Book of Mormon geography. Quotations about Zion appear in a variety of contexts, both in the scriptures and in the words of Joseph Smith and other Church leaders. Zion can be everywhere (Zion is the pure in heart) or in one specific place (Jackson County, as in Zion's Camp, D&C 100, etc.). Even if we equate Zion with the Book of Mormon promised land, that doesn't tell us where Lehi landed and where his descendants lived up until Cumorah. The Book of Mormon promises extend from Lehi's day down to ours. His descendants have intermingled with other people throughout the hemisphere.
I have a detailed paper about this that is a chapter in an upcoming book. It's over 6,000 words, so there's no point posting it here. No one reads long blog posts. Instead, I'll summarize it.
One of the most-quoted references to North and South America comes from a sermon purportedly given by Joseph Smith on July 19, 1840. Here is the version of that quotation included in an article titled “Joseph Smith’s July 19, 1840 Discourse,” published in BYU Studies: