The WTS knows about the importance of the Lunar Three measurements on VAT 4956. They refer to them in footnote 18a on page 28 of "When Was Ancient Jerusalem Destroyed? Part Two," WT 11/1/2011. In that footnote they try to discount the findings of scholars F. Richard Stephenson and David M. Willis, who calculated the Lunar Three intervals on VAT 4956 and found them to be very accurate, to within four minutes (one time-degree).
I wrote about the Stephenson/Willis article on this board four years ago, so I immediately picked up on footnote 18a. Speaking of the Lunar Three measurements recorded by "ancient observers" on VAT 4956, the WTS states, "Such measurements were not reliable."
Stephenson & Willis were impressed that the measurements were accurate to within four minutes; the WT says the "measurements were not reliable." If we go through the Lunar Three calculations step by step in this thread we can see for ourselves whether or not the measurements are accurate.
(I did this once before, back in 2007. I ran the calculations for the year 568/567 BCE and also for Furuli's made-up calendar for 588/587 BCE. The Lunar Three measurements clearly rule out the WT's date.)