If you read it entirely literally, you are entirely wrong from the beginning. And you have given no good reason for reading it that way.
But, if you would insist on reading it literally, then I would have two words for you:
kol erets
This term, translated as "the whole earth", can be used to mean the entire planet, but about 75% of the time in Scripture, it is used to describe a local area, a piece of ground or even a group of people. It is actually only occasionally used to mean the entire planet. The writers did not even have a concept of the planet. It was all flat earth and was encompassing a very small area. So, if the original composers of this text knew that a flood came and wiped out their entire known "world", then kol erets it is. It works fine both ways.
BTW, when the Gospels describe a census being taken of the "whole earth", were they counting the natives in the South American rain forest? Or the folks in China or India? What is your literal reading of that phrase?
But, more importantly, why are you stuck on the literal interpretation. If you insist on refusing to defend such a reading, you can not, with intellectual honesty, go around espousing a literal reading just because it happens to be the style you believe is the right one. If you are going to convince anyone, you had better start giving the basis for your position.