Me too, but think of this. The person probably did not shave his head like JP did. If so, he needed something sitting deep enough to cover the hair. The color, the shape, or bald pate would have been remembered by the witnesses. I have seen overseas hats with flaps on the sides and the back, but the main thing, I think the top part is wedged. This is why I thought about a pilot hat to start with.
My theory still is, either a military brat or the collector of old army stuff. Maybe including knives or whatever he used. I remember when they were looking for DN, they spoke about a machete. I have no clue about machetes, but I’d look at collectors’ cold weapons.