The idea of JEDP in writing of Genesis, with JE being written early, maybe even pre-exilic, would mean some sort of meaningful mentions in other later books, such as we have in dozens of works from the late Hellenistic era. We have name mentions. Noah, for example, in Jeremiah. But nothing of the tale. IF a JE (or a J or an E) surely there would be mentions. 
MY problem is this. Most scholarship accepts the notion that whoever initially came up with the Biblical story of Adam and Eve took it from the mythology of the Canaanite neighbors and the surrounding countryside. It seems as if scholars talk about this “Judaized” version stretching as far back as the kingdom of Israel’s existence. AND that version having been oral initially. I think this would mean that the OT authors would have been very familiar with the Judaized version of the ANE mythology. It seems to me the OT authors were familiar with base ANE mythology, not an oral tradition (or written one) of a Judaized mythology.
This would mean that the sources were very late. Persian or Hellenic.