I have a suggestion.
This is a hat I love very much, and I remember a GM who often wears it too.
This is what it looks like on the side.
On the left is what it looks like in the game.
On the right is the effect that I moved this hat backward one space.
If you are a fussy person, or if you are very fond of this hat, you will find that the hat on the left is indeed a little forward.
I haven't tried what effect it would be to move two space.
If it can be improved, I will love this hat crazy !