This is a restatement and addition to this post.
- Zohar Shemot 9-10: Refers to 1200 years of exile, to be followed by 66 years until Moshiach. 1266 + 3828 = 5094, less than 100 years after the Zohar was published.
- The Introduction to Tikkunei Zohar (with the peirush of the GR"A): Seems to say that it is 1200 + 72, or 1272 + 3828 = 5100. Round number.
The common denominator between these is that these dates are shortly after the publishing of the Zohar. These two basic teachings show up in other places, these two suffice for now.
- Zohar Chadash Maamar al Mechirat Yosef: Says that after Churban Bayit Sheini, there will be 1540 years of Tikkun for Sinat Chinam / Mechirat Yosef. 3828 + 1540 = 5368. After this, it would be 17 years further for Moshiach ben Yosef to begin to stand against Esav.
This would seem to be, per the academic approach, hundreds of years after the Keitz in Zohar Shemot. But this too has the same feature. According to the introduction in the printing that I have, the Zohar Chadash was first published in the year 5351 in Tsefat.
The Zohar seems to have a knack for being published slightly before the "pshat" Keitz that is listed in any volume.
The exception for this is the Keitz of 5408, which as I wrote before, appears to be a late addition anyway. By late, I mean not of the original teaching.
One might think from this that there is a spiritual Tikkun for learning these subjects starting close to their "pshat" dates.