I see that you examined in detail the first half of the Jeremiah pronouncement. But not the second.
Babylon did not die nor become desolate.
I was focusing on the 70 years, how they were applied and when/how they ended. Granted (as we've discussed before I think?) Babylon as a city did not become desolate until centuries later. Babylon, however, ceased to be an hegemonic empire when Cyrus conquered it.