Problems with Bur-Sagale eclipse dated to 763 bc

I posted my message to sci.archaeology and soc.history.ancient almost
two weeks ago but so far no one has been able/willing to answer my
questions there. As the problem is related to astronomical dating of a
historical period I decided people in this forum may help me out.

Astronomers decided that the supposed eclipse in month Simanu mentioned
in eponyms of Ashurdan III with Bur-Sagale in office occurred on June
15, 763bc. However, if we accept this dating of the event we also have
to believe that Nissan 1 that particular year was declared on March 20,
that is 8 or 9 days before the vernal equinox as in 763bc spring
equinox fell on March 28 or 29.

On the other hand, the data we have regarding Babylonian and Assyrian
calendars suggests that they never started their new calendar year
before the vernal equinox.

My point is that either the dating of Bur-Sagale eclipse is wrong (in
that case we'd have to choose the 791 BC eclipse at sunset) or the
statement about Nissan 1 declared by Assyrians/Babylonians on/after the
spring equinox is false.

Could anybody help me solve the puzzle?