Somehow, when I believe I'm being clear, I'm not. My comments regarding the use of the conventions J and P (etc.) was to clarify that I'm not clinging to the Wellhausen form of source criticism. Yet the sources are distinct and my use of the labels is referent to the blocks of text not the hypotheticals associated with them.
My comment was in response to the suggestion that individual sources can be linked to Babylon more intimately than others. All the sources appear to have been active during and after the exile. (using older short legend and motifs) It's entirely possible they were near contemporaneous camps of scribes. It's been argued that an extensive narrative such as was created through the merging of individual compilations best fits the Greek period, as literature of that nature was unknown prior. It was also the beginning of the era of fastidious scribal copying, which fortunately prevented extensive improvements on the final composition, thereby enabling us to perceive some of the document's history.
The J story, whether you accept Freidman's belief that it was the backbone of the Pentateuch or not, betrays a nuanced talent, that to my understanding, resembles later Greek philosophical reuse of epic and satire. Perhaps I am reading too much into it.
The Bronze Age collapse might well explain the opportunity for local kingdoms in the Fertile Crescent to get established and likely was the ultimate source of certain threads of tradition in the Primary History, but I was focusing on the 5th to 2nd century as the period of advanced literature and philosophy reaching Palestine, Alexandria and Babylon.