Lore,
Lots od assumptions there, but ok, lets for arguments sake say that thos enumber sare ALL correct, with no variance at all ( getting into WT territory there, LOL), we have the period of 2200 BC for a flood in the area of where Noah lived, Mesepotamia.
So, what that means is that the bible writers believed that, around that time period, a great flood ravaged the "whole world".
Was there any flood in that area at that time?
The king's list, for example, mentions a great flood and it is dated to that period.
The epic of Gilgamesh, though older, would have quite possibly mad epart of the flood story.
BUT you are quite right that IF we take the geneologies literally and concretely, we have an issue with taking the flood as a GLOBAL event.