I am not sure we should discard the concept so quickly. Your position,
if I infer all the points correctly, presumes that at some point in time
the 13 lunar cycle year was abandoned for a solar year. Who is to say
that the transition was not protracted and muddled? Perhaps some
peoples converting systems (or vacilating between systems for a period)
before others and the result was a long period of dating confusion. The
Gregorian/Julian switch would me a "modern" (ya) comparison. With all
its organised deliberation, it still caused problems.
Besides, muddled protraction is so human. At least from my
observational experience. Besides, why are we to presume God's dance
with us in history should be found neat and tidy, when it is, after all,
people, He is dealing with?
Just some thoughts. Lest we forget who we are.
-- Brian W. Neuschwander