Gn 1:1-2 In the beginning, when God created the heavens and the earth, the earth was a formless wasteland, and darkness covered the abyss, while a mighty wind swept over the waters.The word translated as "waters" in Gen 1:2 can also be rendered as "vapors". (Which strikes me as how one might describe the nebula out of which the solar system was formed, by the way.) There is no contradiction here nor any need to suppose a second writer.Gn 2:4b-5 At the time when the LORD God made the earth and the heavens, while as yet there was no field shurb on earth and no grass of the field had sprouted, for the LORD God had sent no rain upon the earth...
Was there water in the beginning as the first account says, or no water as the second account says? Was there land as the second account says or just a formeless wasteland covered by water as the first says? Which is it?
Also from your examples...
---In the first, God is called "God".The word translated as "God" is "Elohim"; literally "Gods". (The Jews have always understood this use of the plural to describe God to be "qualitative" rather than "quantitative". To Christians, this use of the plural and the traditional Jewish understanding of its use are suggestive of the nature of the Trinity.) The phrase "The Lord" is used whenever the name of God appears in the original text. Again, no contradiction nor evidence of a second writer.---In the second, God is called "the LORD".
Your basic premise, however, is correct. Different writers at different times wrote the various books. But the writers' works aren't intermingled as you suggest.