'scholar':
You are not very smart, are you?
Quite smart, and significantly more than you.
The tablet indicates that a certain eclipse namely 15th Simanu which can fit the eclipse dated July 1 588 BCE.
Note that 'scholar' inadvertently or dishonestly says the 15th day of Simanu was 1 July, but the Watch Tower footnote actually says "If the eclipse fell on July 15, 588 B.C.E. according to our Julian calendar, then the first day of Simanu would be June 30/July 1, 588 B.C.E." But Simanu never begins in July. 1 Simanu always corresponds to part of May or June.
The Babylonian month Simau is the third month
Yes. Yes it is. 1 Nisan = March/April. 1 Aru = April/May. 1 Simanu = May/June. (I am, of course, aware that if you go back a few thousand year earlier than the Neo-Babylonian period, then the difference between the Julian and Gregorian calendar systems can shift the months outside that range, but that is irrelevant for the period in question.)
so 588 BCE is now properly considered for Neb's 37th year
Definitely not, despite your attempts at mangling the Babylonian calendar in imitation of the Watch Tower Society.
with a 20-year difference between 586 and 588 BCE.
Okay, probably a typo, but that just makes you look kind of dumb.
Thus 607 BCE is firmly established based on historical, biblical and astronomical evidence.
No, you've just further provided more evidence that 607 is definitely wrong.