Hi Bart,
In the absence of a king's name, it is still an assumption to believe a far later king's time (i.e. Darius) was meant. He's first mentioned in chapter 4. Yes, it is hard to untangle the timeline with all the parentheses added to the book, but it is more natural to think the writer, having not specified a new king's name, was still referring to the time of Cyrus.
I find Dr. Constable's online commentary helpful here (noting the table on p. 10).
Regarding Hag. 2:15. Maybe he's using prophetic hyperbole - after all, Haggai 1:12-15 indicates that the people had listened and had already started work on the temple a few weeks earlier than his statement at 2:15, so surely some stones had already been placed on other stones. Yes, 2:18 is phrased awkwardly and must be seen in the light of Ezra and Haggai's earlier statements.
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.
The WT has a very outdated view on this.
*** w06 1/15 p. 18 Highlights From the Book of Ezra ***
PERSIAN KINGS FROM 537 TO 467 B.C.E.
Cyrus the Great (Ezra 1:1) died in 530 B.C.E.
Cambyses, or Ahasuerus (Ezra 4:6) 530-22 B.C.E.
Artaxerxes—Bardiya (Ezra 4:7) 522 B.C.E. (Assassinated after
or Gaumata reigning only seven months)
Darius I (Ezra 4:24) 522-486 B.C.E.
Xerxes, or Ahasuerus 486-75 B.C.E. (Ruled as
coregent with Darius I from
496-86 B.C.E.)
Artaxerxes Longimanus (Ezra 7:1) 475-24 B.C.E.
[Footnote]Xerxes is not mentioned in the book of Ezra. He is referred to as Ahasuerus in the Bible book of Esther.
Instead of renaming kings (without any support from history) and squashing them in in chronological order before Darius, it makes more sense to understand that the writer of Ezra began a giant parenthesis at 4:6 - as if he's saying, 'While we're on the subject of opposition to our temple rebuilding, I might as well mention what happened later in Xerxes' and Artaxerxes' reigns about our city rebuilding.' Then at 4:24 the writer resumes the narrative about the temple rebuilding.
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.
There are different ideas about this, including one that the two names refer to the same person, but 1 Esdras 6:18 and 1 Chron. 3:17-19 suggest otherwise. Sheshbazzar (var. Shenazzar) appears to have been Zerubbabel's uncle so they both could have been the 'go to' guys, or for some reason Zerubbabel took over responsibility.