Have you tried shooting from different angles? More from above, more from below? Just to try to get a different perspective on it? Focus on the shapes, curves, angles and shadows and see if that makes a difference. Since your subject isn't moving you may want to try a tripod and longer exposure rather than the flash since you said you had problems with the flash washing the hat out. I wouldn't mind the line created by the table if it were kind of more abstract maybe because then it would be yet another part of the pattern of colours, etc.
