Bart,
The Darius mentioned in Haggai is Darius I (522-486 BCE). WTS and conventional chronologies coincide here.
*** Insight Vol. 1, p. 583 Darius ***
It is particularly with regard to the rebuilding of the temple at Jerusalem that Darius Hystaspis figures in the Bible record. The temple foundation was laid in 536 B.C.E., but rebuilding work came under ban in 522 B.C.E. and “continued stopped until the second year of the reign of Darius” (520 B.C.E.). (Ezr 4:4, 5, 24) During this year the prophets Haggai and Zechariah stirred up the Jews to renew the construction, and the work got under way again. (Ezr 5:1, 2; Hag 1:1, 14, 15; Zec 1:1)
*** Insight Vol. 1, p. 1019 Haggai, Book of ***
Date and Circumstances. The four messages recorded by Haggai were delivered at Jerusalem within about a four-month period in the second year of Persian King Darius Hystaspis (520 B.C.E.), the book apparently being completed in 520 B.C.E. (Hag 1:1; 2:1, 10, 20) Zechariah was prophesying for the same purpose during Haggai’s prophetic activity.—Ezr 5:1, 2; 6:14.
*** Insight Vol 2, p. 613 Persia, Persians ***
The temple work then lay idle “until the second year of the reign of Darius the king of Persia.”—Ezr 4:24.
Darius I (called Darius Hystaspis or Darius the Great) evidently engineered or instigated the slaying of the one occupying the Persian throne and gained the throne for himself. During his rule the temple work at Jerusalem was renewed with royal approval, and the temple was completed during his sixth year of rule (early in 515 B.C.E.). (Ezr 6:1-15)
Not sure where you're going with Isa. 61.