(Make sure to read all posts on Birkat HaChamah here)I have seen recently some quotations from the GR"A's peirush on Sifra Ditzniuta that try to suggest that the coming of Moshiach is related to the year of Birkat HaChamah. Allow me to translate the section in question.
And this revelation, it does not have an [exact] known time, "heart to the mouth it is not revealed", but rather it is known that during the entire 5th millenium it could not come, in the secret of the entire day of "ו"ה" (Eichah 1), and it will only be revealed in the 6th millenium which is in the secret of the the Livyatan that was mentioned, and that is what is written (in the Zohar on Va'Era) 1 for 1000 days, that is to say in one of the 1000 years he will be revealed. And it says small days, because just days (alone) is 1000 years in the secret of the 6 Days as was mentioned, but small days is one day which is days of Malchut Chochmah Z'eira, and that is days that is mentioned in the Torah "days will be the Geulah" (See Vayikra 25:29). That is to say that one year will be the year defined as the Geulah, and it is the year after Shmitah, in which that is the time of Chesed, and then will be revealed the פום אמה and Moshiach will come. And that is what is written in the Zohar on the small aleph of the word Vayikra, that it is Malchut, in which the letters are small, and that is the 1000 pieces that Moshe took and left one which is the small Aleph. Aleph (meaning 1) from 1000 and that is Malchut Atarah that there it is revealed.
We can see from this that the GR"A is writing that the exact date is not known, but a certain single year in the 6th millenium will be so momentous in its events that this one single year will be called the Year of Geulah. This year will be the year after Shmitah. The GR"A uses similar language to what he used elsewhere, speaking about Chesed being revealed in פום אמה, and talking about the Atarah. He is talking about the fact that the year of Moshiach's revelation B'itah will be the year that the world reaches the level of Ateret HaYesod, as I mentioned in Shiur Yemot HaMoshiach. No one has claimed that this spiritual event has anything to do with the year 5769.
And for those who are wondering, yes, the year 5783 that is mentioned in Shiur Yemot HaMoshiach is the year after Shmitah.