(Make sure to read all posts on Birkat HaChamah here)
I do not believe that one can really begin to understand the sod of Birkat HaChamah without learning Pirkei D'Rebbi Eliezer about the solar cycle.
Particularly chapter 6 discusses, in a rather cryptic way, the correlation of the sun and the moon. The internal contradictions point to something very deep. (Please note in some printings it is chapter 6, others it is chapter 7. The chapter starts with the words Rabban Yochanan Ben Zakkai)
On the one hand, the exact halachic length of the lunar cycle is mentioned. However, there is a cycle concept introduced for the Molad progression. Namely, if we take the Molad to occur at the hour of a certain planet, like Shabbtai, for example, which one will it land in in the next month, and twelve months later?
In order to give over this answer, we must assume round numbers of hours. This is in the exact same chapter where we are told the length of the month down to the number of chalakim.
We are shown that if we assume no leap years (i.e. every year is always 12 months, no Adar II), that the Moon has a cycle of 21 years.
Now, as an aside, we see here that the first Molad is taken as the same moment that the Sun was created, i.e. Tuesday night 6pm, the day of the Spring Equinox, not in line with our system of calculating the Molad, based on the first Molad to have occurred by the end of Elul, BaHaRaD.
So the beginning of the 21 year cycle and the beginning of the 28 year cycle start at the same moment, what is the logical thing to do? That would be to determine the point how often the two cycles start at the same time. The earliest amount of time for this is 84 years, because 21 * 4 = 28 * 3.
We have now introduced an 84 year cycle to the mix. But what is it based on?
84 years * 365.25 days, we get 30681 days.
84 years * 354 days (approximate lunar year length), we get 29736 days.
Subtract one from the other and get 945 days differential. So the significance is not that the events occur at the same time at all (or in the same calendar year).
That all being said, it is further asserted that 84 years is the time it takes for one hour to pass for Hashem. If we take 1000 years and divide by 12 hours, we get 83 and a 1/3 years per hour, a value stated explicitly in chapter 48.
That, however, doesn't necessarily explain 84 years. The math presented is contradictory. Every 84 years they line up. Is that 84 lunar or solar years? I would theorize that we are directed to make a brachah on the solar, and not the lunar. The solar takes precedence. The number 84 is 12 times 7, the 7 leap years and the 12 simple years, the 19 year cycle.
That is part of the sod.