Yeah, we're somewhat agreeing. The trick is not to read Chapter 1 as being continuous with Chapter 2, but that there's a natural break in the 'story-telling theme' partway through 2. By any metric, it's a bit confusing, but that's all it is, a bit jumbled.
It's two different stories with two different purposes. Read literally, there are internally inconsistent, which creates obvious problems for Biblical literalists (see the consistency in the order in which things are created relative to man).
The first story is about the nature of God and how He creates the world. It is a testament to the power of God.
The second story is about the nature of man and the relationship between God and man. That relationship is about God and named individuals, Adam and Eve.
In the first story, God creates man (side note: contrast that God "created" man, implying labor, but brought the animals and other parts of creation into being through words). However, in the second story, God creates Adam and then breathes into Adam the Breath of Life. That's a much more intimate means of creation than the first story. It is an investiture of divinity via a kiss.
In the first story, God grants man dominion over the Earth, but man does not respond. The communication between God and man is strictly one way. In fact, from the first story you would assume that God becomes a passive onlooker as to the actions of man; that is He creates man and then doesn't do anything else with man. In contrast, the second story has ongoing dialogues between man and God, and God takes an active interest in the actions of man after man's creation.
In the first story, the directive to go forth and multiply is given as a matter of fact direction; that is nothing special after creation is necessary for man to do this. Sex in the first story is divinely directed, but mundane. In the second story, the union between man and woman expressly becomes a gift from God. Sex becomes spiritual.
As mentioned, in the first story, God gives man dominion over the animals, but in the second story God creates the animals specifically to help man and allows man to name the animals. This naming, the use of language, references back to the use of language by God to create the world in the first story and back to the investiture of the Breath of Life into man in the second story (can't speak words w/o breathing, after all). This is indicative of the unique nature of man to not just communicate, but to communicate in abstractions. Of course that power to communicate also enables communication with God, which, as we've seen, occurs only in the second story.
In the first story, there is an idyllic world with no strife. However, the second creation story has an inherent flaw: the free will of man to disregard God's will.
Both free will and the ability to communicate with God are necessary antecedents to the creation of the Covenant with Abraham. Without either the Covenant would be meaningless.
The first story harkens back to earlier beliefs of an uninterested sky-father god who created the world and then left it to its own devices. The second story, with the intimate relationship between God and man, lays the ground work for the Covenant with Abraham.