The timing is purely coincidental, but it is an interesting historical fact that people in New York were reading Letter VII which explains that the Hill Cumorah is in New York right about the time that Joseph was sealing his testimony with his blood in Carthage.
News traveled slowly in those days. On June 29, 1844, L.O. Littlefield wrote a letter from Nauvoo describing what had happened in Carthage. He sent it to the Editor of The Prophet, but it wasn't published until the July 27, 1844, issue.
The June 29th issue also announced that William Smith was the editor of The Prophet.
It's interesting that the first issue of The Prophet, published in May 18, 1844, included Oliver's Letter I. The paper showed how significant these letters were to members of the Church in Joseph's day by introducing the letters with this statement:
"As the important particulars, and incidents, connected with the coming forth of the Book of Mormon, have ever been, and are now, subjects of enquiry, we shall insert, for the benefit of those who are not acquainted with the coming forth of the above named work, one of the following letters, each week until we are published."
Each subsequent issue published another of his letters.
My point here is that although Oliver's letters had been published four times already (1835 - Kirtland, 1841 - Nauvoo, 1841 - Philadelphia, and 1844 - England), the editor of The Prophet thought they were so important that he republished them yet again, this time in New York.
The June 29th issue happened to be issue no. 7, which is why it contained Letter VII.
A fascinating coincidence, isn't it?
Some readers may not be familiar with The Prophet. Here is an explanation from the DVD that accompanies Susan Easton Black's excellent book titled The Best of the Prophet.
Susan Easton Black
Here is an excerpt from the book, pages 7-8