After a few more hours of staring, I think the pattern I originally published was incorrect.
Does this look better?
Those white diamonds are clearly smaller than the white triangles. I think this is closer. It's still not right, though. Notice that the white diamonds are close to touching in the enlarged photograph. Perhaps the white diamonds are flatter (and thus, smaller) than the triangles.
Or, perhaps the hat is decreasing by that point, which would make it much more difficult to recreate the pattern. Right now, I am making the assumption that decreases begin after the design. Hrm. I think I'll be mulling it over and staring at it for a few more hours.