'scholar':
You introduced Stern so if there is a contradiction in his statements then that is not my problem.
There is no contradiction in Stern's statements. Most of the towns were destroyed, and the towns that were destroyed were not resettled throughout the exilic period. Some other towns were not destroyed and remained populated. If you imagine the statements to be contradictory, you quite definitely have a problem.
You need to focus on the fact that the judgement of Babylon only occurred after 70 years was fulfilled and that was not at its Fall in 539 BCE any other interpretation is fanciful. Also, the verse clearly indicated that the land of Babylon would also be desolated which did not happen in with the Fall.
Complete nonsense. The claim that Babylon was 'called to account' in some manner in 537 BCE is plainly stupid, and the land of Babylon wasn't desolated in 537 either, further invalidating your claim. Daniel 5:26-31 (written later but consistent with how the Jews regarded the period) quite clearly refers to the end of Babylon's days and being called to account when it was conquered in 539.