What is your view on relying on the Cyrus Cylinder, to accept 607 as the correct date of destruction. ...
... I'm primarily interested in the appropriateness of using the Cylinders date of 537 + 70 = 607
You cannot rely on the Cyrus Cylinder to prove or disprove 607 BCE as the date of Jerusalem's destruction. It is undated and tells how Cyrus conquered Babylon, got rid of incompetent Nabonidus and brought peace and religious harmony to the land, etc.
You have to go to other sources to derive any dates. The Nabonidus Chronicle indicates Babylon fell in Nabonidus' year 17. Astronomical texts anchor dates for certain kings' years and other kings' years can be derived from kings' lists. Babylon fell in 539 BCE as Over%forme said.
Next you have to determine what the prophesied '70 years' relate to. Jeremiah consistently relates them to a period of Babylonian domination over the nations including Judah (Jer. 25:8-12; Jer. 29:10 - '70 years for Babylon'). The Babylonians were defeated in 539 BCE, therefore their domination of the nations ceased in that year (2 Chron. 36:20, 21; Jer. 25:12).
The first period of seventy years spanned from 606 BC until 537 BC, known as the Babylonian Captivity.
The '70 years' could be a rounded number (Nineveh fell in 612 BCE; 605 BCE was the battle of Carchemish, defeating the Egyptians, and Babylon swept down taking Palestine) or can literally fit from 609 BCE when the last king of Assyria was defeated and the last Assyrian stronghold, Harran, was razed to the ground. The Babylonians had hegemony over the nations from that point. 609 BCE to 539 BCE = 70 years for Babylon.
The second period of 70 years came 19 years later from 587 BC until 518 BC, which was known as the period of Jerusalem’s Desolation's . On the 9th of Av 587 BC, the Temple was destroyed by Nebuchadnezzar.
We agree on the year of Jerusalem's destruction. The Temple wasn't finished until Adar 517 BCE (Ezra 6:15) so yes, the Temple was desolate for 70 years.
You're looking for another Bible chronology/prophetic 'Gentile times' fit with Israel's independence, aren't you? There'll be a whole lot of scriptural hopping, skipping, jumping and eisegesis to find one but good luck!