AnnO Haggai, during the 2nd year of Darius, claims that Jehovah states that his house is still a waste whilst the returnees have build their own own homes 1:9. This shows that the returnees have made no effort to build his house but have built their own instead, and planted crops which Jehovah with held the dew from. He continues to say that Jehovah then rouse up the spirit of Zerubbabel and Joshua and all the people and then they began the work on his house. This indicates that this was the first they did any work on the house, other wise he would have said continued.
This is made clear by Jehovah's statement at 2:15 from the 24th/9th/2nd " from this day forward, before there was the placing of a stone upon a stone in the temple". No work had been done no stone on stone, unti the foundation stone was laid on that day 2:18.
From Haggai it is clear that work on the temple started in the second year of Darius for the first time.
I agree with you that Ezra 3:8 links directly with 3:1,6, however Ezra does not state that the event after chapter 1 were during the reign Cyrus they are in fact undated and therefore we must look elsewhere for the date, but he does states that the returnees of chapter 2 did not include Sheshbazzar the govener, in those lead by Zerubbabel, but again Ezra does not tell us his capacity, which agrees with their later arrival , and Haggai.
As regards chapter 4 the chronology is a mess due to very poor redaction, and I do not know how this viewed in WT land. However what is clear is that 4: 1-4 follows the chrono of Haggai. As Sheshbazzar was made governer by Cyrus Ezra 5:14, why do the adversaries of 4:1-2 speak to Zerubbabel and not Sheshbazzar, this does make perfect sense though if this happens when Zerubbabel is governer as sated at Haggai 2:21.
(1 Esdras from the LXX gives a much better understanding of the true timing of events.)
I take your point regarding the second arguement re the Jubilee, but it does work and is more justified for 587 if the laws regarding release from Deuteronomy are applied for an exact timing, pointless to use that here as you say the 586 basic explaination is complicated enough.
Thanks for your input thus far,
BB