As I understand it, the end of the last remnant of the Assyrian empire was in 609 BC, which seems to fit fit very nicely with 539 BC as the end of the Babylonian empire. Is that correct?
The collapse of the Assyrian empire certainly had a major role in the rise of Babylon as a regional superpower. However, if you are looking for a period to match the biblical 70 years, that is not a likely choice, because the beginning of the 70 years is bionically linked to Nebuchadnezzar. As I see it, there are 2 main alternatives for reconciling the biblical 70 year period with secular history:
(a) the 70 years is actually 68 years, beginning with Nebuchadnezzar commencing his domination of the region - a mainstream view held by religious scholars, at least back as far as Bishop James Ussher, writing in the 17th century; or
(b) the explanation given by Doug Mason, above.