Bluegrass,
I do not have the space here to put the reasoning behind the positions I put; so I suggest that you come back to me after you have read the book I referred to. It is inexpensive and very easy to read.
It has long been agreed that these two accounts of Creation are separate and independent. The Elohist story begins (NIV): "In the beginning God created the heavens and the earth" and at Genesis 2:4a ends the story in similar fashion. The Yahwist story however begins the other way around at verse 4b: "When the LORD God made the earth and the heavens". The author of Genesis 1 was so determined not to copy the story that sat in front of him/her that the sequence has been reversed.
I suggest that we should applaud the literary skill of Ezra when he combined these accounts in such a way that some think that chapter 2 is a comment on chapter 1. His great skill is further exemplified in the two Flood accounts that he weaved together to produce an apparently single record of the Flood.
So I suggest that you put your assumptions aside, without concern at the potential outcome of your genuine investigation, and make your own study and come to your own genuinely held beliefs.
Someone had to write these stories, but they were not there to record what happened or what was said. Also, remember how those people used history in a way so that it influenced their own community. They did not write objectively. Their records of history were theological documents.
All the best for your study,
Doug