Genesis 1 and 2 are a battle-ground for biblical creationists vs. other biblical creationists. It's confused me many times.
I feel like after Gen 2.1 or 2.2 another author picks up the strain. But being a fundamentalist-type this caused me problems not unlike reading Matthew vs. John in the Gospels.
Obviously the creation strain has taken up a new perspective in Gen 2.2. The question is: Is Gen 1 and 2 contradictory any more than Matthew and John are contradictory? Matthew for example writes about a Messiah-King, John about a personal Saviour.
Greater divisions of thought (denominations) have sprung up because of supposed contradictions.
I had to read Gen 1 and 2 about 2 hundred times (with much prayer) before reconciling the 2 chapters unto my own conscience.
Could I re-write a better mechanism of creation? No way! Chapter 1 (like the book of John) leaves ample wiggle room for metaphysical events, including 3 creation ("Bara" in the Hebrew) events. Chapter 2 takes on other metaphysical events: Like the formation of Eve.
Later in the book of Psalms (139 I believe), man is curiously seen wrought in the lower parts of the earth when as yet his members were not yet written.
At present, I detect no valid contradictions between Gen 1, Gen 2, and the book of Psalms, unless one interprets them materialistically.
(Note. I repeatedly make the same mistake of interpreting materialistic events for metaphysical events, too.)