I think you're asking the wrong question, HD. I think this chip will work well from exactly 12V. But then you say you're using batteries, which will only be at exactly 12V for about, oh, 3 minutes after turning the power switch on. They drop from there as they discharge.
I make this point because if you were to use a wall power supply that gave 12V, I wouldn't worry at all. Sure, a smidge more voltage might help a bit, but at 12V, you will have gotten rid of all the nasty clipping on high musical peaks with demanding headphones.