These two posts relate to particular years in our generation, and for Sprouting, I have selected a starting date, Yom HaAtzmaut. There is also a starting date for the second. Between 2449 and 2503, everything revolved around Nissan. So too it is proper to relate to the dates in our age as such, so the 1st year under Yehoshua would be Nissan 5768 to Nissan 5769 (rather than the plain 5769 that I wrote there), more or less corresponding to the 5768-5769 fall of the Erev Rav written about in the Sprouting of Moshiach.
Since the dates are so close, I would prefer to give it a less definite starting and end point, and say that the starting point for each is Pesach of a year, and the end point is Shavuot of the following year, thereby encompassing the Omer. Therefore both of these counts would, for this year, be from Pesach of 5768 to Shavuot of 5769, etc.
I may or may not update both posts to reflect this.