Pretty normal for cascade shadows to have artifacts like this. You'll often see this kind of gap/artifact on hats in video games from the last 2 or 3 generations. You might be able to design around it by making the windows their own model with depth going into the wall.
That is clearly a Fedora such as would be worn by an adventurer like Indiana Jones, NOT a cowboy hat... You guys call yourselves hat makers... Valve would be disappointed.
Looking good so far. It definitely has a ton of character. Just an idea, but seeing how everything else is exaggerated except the hat, why not exaggerate the hat?