Thats actually less of a texture thing and more of a model thing, that's how alpha cards work. Not much you can do about that, except rotating and moving some of the cards around or adding more of them. No matter what, you are going to see those cards crossing some where. (Cards Colliding with the Geometry for the tail, and + from the back)
/em points at beastmen moogle mount.
Crude example I whipped up for what you are seeing.
Surprised they don't have a gloss/shine slider tbh. I haven't looked at the character creator in a while.