NOTE: the client is saying they probably want this logo to be embroidered above the hole in the back of a standard baseball cap... I can adapt most of the entries so far to this application... but you might want to think about this for the designs going forward.
here is a link to an image showing this embroidery area for your reference - the back area or maybe the front... but he has this image of something on that curve... (it is a bit flexible too)
https://drive.google.com/file/d/0B0q1jFIQTqowT0tjT2d4c0xoUE0/view?usp=sharing