There must be something in the story that says that God created everything from nothing. As far as I know, the Jews, who use the translation that you like and want to use, believe that God created everything from nothing.
There is nothing in the story that says that the substance of the earth and/or waters were already in existence.
The fact is that both the translations say that God created the heavens and earth, not that God made the heavens and earth from pre existing material.
You tell us here that your interpretation is based on the assumption the Bible has to mean what other cultures of the day believed. You assume the answer, that the Bible must mean what other cultures believed. That is circular reasoning, esp when the Bible does not say that.
The Biblical cosmology that we are told the ancient Jews believed is one thing but the cosmology that we can understand from what we have learned from science, can also fit with what the Bible tells us. There is nothing wrong with being informed about Biblical interpretation through science.
Day 2 says that the waters were above the sky, and in those days the clouds, and whatever other waters there were, were probably above the atmosphere to a degree. (esp going by Job 38:9 which gives a picture of clouds extending quite a distance from the earth, and why not when there would have been no atmosphere to stop that from happening).
Sites like these show that science (even though it is still theorising) might be on the right track when it speaks about clouds around the early earth which allow light in but not necessarily allowing the sun and moon etc to be seen clearly.
Solution to 'young' sun paradox proposed through thinner clouds on early Earth.
www.space.com
Our planet flipped back and forth between a thick haze and clear skies 2.5 billion years ago
www.newscientist.com
Climatologists have a Precambrian problem: early in Earth's history the sun was dimmer, but the Earth wasn't colder.
www.uvic.ca
Our planet flipped back and forth between a thick haze and clear skies 2.5 billion years ago
www.newscientist.com
Gen 1:1 tells us that God was creating the heavens and the earth. This means that God was creating the early stars, sun, moon etc.
Darkness was on the ocean on the earth and thick clouds covered the earth and God began to allow light through the clouds. Then on day 4 the sun and moon etc could be seen more clearly and phenomenologically (which is the language used in the Bible a lot) the sun, moon etc then looked to be in the atmosphere (just as phenomenologically the sun looked to be going around the earth and was spoken of that way).
The phenomenon of the sun, moon and stars looking to be in the atmosphere and below the transparent clouds was not the case all the time however and these days the clouds cover the sun, moon etc when it rains.
I'm just demonstrating that the Bible can be read to indicate agreement with science at the moment in the hisory of what science could be telling us.
As I said, Gen 1:1 indicates that God was creating the heavens on day one, and so the sun, moon etc were also out there in an early stage of creation, just as the earth was in that early stage of creation.
I am not making an assumption about the Genesis story being compatible with modern concepts of cosmology and I have sort of demonsrated that. But you have said that you are assuming that the story is wrong and that it has to agree with what some other cultures said about cosmology.
It's cosmology can be read to agree with science and to even be illuminated by science. Why would you then assume that the rest of the creation story got it wrong?