Here's a take on the story you may not have considered. The Flood stories are dropped into and interrupt the narrative. They form a section (6:5-9:19) of material that identifies Noah as a Flood hero rather mashed together.
It was apparently dropped here because the narrative mentions a Noah as a vine grower who invents wine and takes away the curse on the ground by providing "comfort". (5:29) (9:20,21) The meaning of his name.
Different traditions about a man named Noah, one the flood hero, the other a farmer who brings consolation from the curse on the ground by making wine. Remove the section and the narrative flows unbroken and eliminates all the contradictions created by its insertion. The 120 years lifespan limit, the Nephilim appearing after the flood, Nimrod as one of the "mighty" men/Nephilim.
Interestingly the isolated tower story (9 verses) also was sewn into the narrative without any real continuity. The story was a short origin tale explaining languages through the clever play on the Hebrew word bālal "confuse" and the name of the Akkadian city 'Babel.
The connection to Nimrod is made by readers only because Babel was said the beginning of his empire. Nimrod is not part of the tower story at all. The mention of the city Babel offered the compiler an opportunity to drop this short tower legend into the narrative just like he had done with the Flood story.