You're right that we have a different web of concepts and emphasize different abstractions than other cultures did, but this bit paints a really misleading picture of who we're talking about and how sophisticated their ideas were:
> Ancients, without all the distractions and knowledge we have now, might have been much more attuned to their emotions. They’d likely need to be in order to survive by following intuitions and responding to low-level feelings of fear.
There's very little difference in the amount of "knowledge" between any two cultures, or really even between any two people. One culture's collective knowledge may be more reliable or more demonstrated or more productive (by some measure), but everybody's always walking around with a head 100% full of knowledge.
It's a mistake to think that Mesopotamians, Babylonians, and Greeks were "surviving by intuition" under "some low-level feeling of fear". Like us, they were building huge cities with complex trade networks and economies, with obscene bureaucratic processes and people so specialized in craft and work that their whole lives were committed to studying or teaching or keeping account balances in order.
They had rich, interwoven systems of knowledge, and the ancient Greeks in particular fancied mechanics and abstractions much the way we do -- a similarity that exists largely because we openly modeled much of modernity on their culture.
When hepatocentrism prevailed among the Greeks, it wasn't in the context of some scared, emotionally volatile people making do in caves beset by tigers and lions or something. It was in the context of highly educated urbanized people drawing sensible conclusions based on what their culture happened to emphasize in its own web of thoroughly mechanical and abstract concepts.
Some of your suggestions about what facts they were integrating are probably right and many of them are fun to speculate about, but whatever they were, they were being fit into a much more elaborate and abstract schema than you're giving credit to. These were not inbred bumpkins or wild primates making cute guesses and enshrining them in mysterious lore. They were scientists and physicians living and studying in ways not all that differently than our own, and their discoveries were being encoded into myth by the esteemed, committed poets among their aristocracy in much the same way that screenwriters and novelists work modern knowledge into their stories.