Hi David,
We need to know for certain the dates of Ezra's and Nehemiah's activity and which Persian kings they served. There is no explicit statement linking the public reading of the Torah by Ezra, which to all appearances looks like a shemittah year, to a specific regnal year of a king of Persia. One cannot just assume Neh. 8:1ff records events of the regnal year mentioned in Neh. 2:1. And we do not know if Artaxerxes I is the king mentioned in Neh. 2:1. It could be Xerxes per Josephus because Jewish literature treats "Artaxerxes" (Achashverosh) as a title. These and other problems beset attempts to use the Ezra-Nehemiah narrative to fix sabbath years in the early post-exilic period, so it is not a given that 445 BCE was a shemittah.
Your theory that a cycle beginning in 515 BCE was interrupted by Antiochus IV Epiphanes and a new cycle was put in place in 164 BCE when the Temple was cleansed is interesting. However I think 515 BCE was the second year of a 7-year cycle. 2 Chronicles 36:19ff implies that the 70th year of the destruction of the First Temple was a shemittah year, that as long as the land of Israel was without its Temple (not just without its people) it remained "desolate" and enjoyed its sabbaths. From the destruction of the First Temple in 587 BCE to its rebuilding in Year 6 of Darius I in 516 BCE was 71 years. So 517, the 70th year, was a shemittah and 516, the 71st year, was the end of the desolation and the first year in a new 7-year cycle. I don't see this as a new count because there is no reason to believe the count was lost or discarded, just as the seventh day was never lost or discarded even if it could not always be observed in the Exile. There is evidence of a resumption of the actual observance of the shemittah with respect to the land, but no evidence of a completely new calendar for shemittot at this point.
But yes, there are shemittot recorded for the years 163 BCE, 135, BCE, 37 BCE, and one in 55 CE, and this cycle cannot be extended back to agree with a shemittah falling on your date of 515 BCE or my date of 517 BCE. This is probably the reason why. Originally a 50-year cycle was in force where the 50th year was a year unto itself, a Yovel, and not the 1st year of a new cycle. The Torah states that the land is to be worked six successive years and left alone on the seventh, i.e. the shemittah. If the Yovel had never been a year unto itself but the first year of a new 7-year cycle there would be times when the land was worked just five years which cannot happen. At some point in the post-exilic period (I think under the Greeks) the Yovel became the first year of a new cycle and the last year of the old but it was no longer observed as a shemittah, which meant the land was still worked six years.
System 1, Pre-exilic (8 sabbath years in 50 years):
1,2,3,4,5,6,7(shemittah),8,9,10,11,12,13,14(shemittah),15,16,17,18,19,20,21(shemittah),22,23,24,25,26,27,28(shemittah),29,30,31,32,33,34,35(shemittah),36,37,38,39,40,41,42(shemittah),43,44,45,46,47,48,49(shemittah),50(shemittah),1,2,3,4,5,6,7(shemittah),etc.
System 2, Post-exilic (7 sabbath years in 50 years):
1,2,3,4,5,6,7(shemittah),8,9,10,11,12,13,14(shemittah),15,16,17,18,19,20,21(shemittah),22,23,24,25,26,27,28(shemittah),29,30,31,32,33,34,35(shemittah),36,37,38,39,40,41,42(shemittah),43,44,45,46,47,48,49(shemittah),50=1,2,3,4,5,6,7(shemittah),etc.
System 2 is reflected in the years 163 BCE, 135, BCE, 37 BCE, and 55 CE. So what you (and I) could argue is that somewhere between the late 6th and mid-2nd centuries BCE, System 1 was replaced with System 2. After 70 CE System 2 was eventually replaced (by the chronology of Sabbath years in the Seder Olam Rabbah) for the system we follow now in the land of Israel. BTW, a shemittah is currently in progress.
Regards,
Tory