>The Iliad doesn't actually fit the geography or the timeline very well.

Fits it well enough to find at least one city based on the descriptions in the book, and the existence is others is supported by other evidence. It gives accurate names to towns and cities that had but existed for hundreds of years and the clusters of cities mentioned being near each other are, in fact, near each other.

>Also the people in the Iliad are physically bigger than humans, there are talking horses, and gods directly intervening. It is not a historical document.

Don't be obtuse, stories often take inspiration from historical events and then embellish them for entertainment; it's an epic poem not a history book, history didn't exist as a thing to be studied and cared about until Herodotus. No one thinks Achilles was out there fighting a literal river god, but a large conflict between a unified Greece and the city they called Troy some time around the bronze age collapse is highly plausible, given supporting evidence from Hittite and ancient Greek sources.