The .496 is normal for a plastic 1/2" hex.

But .560" (14.2mm) isn't even close to 12.7.
On the other hand, 0.560" is the standard hex size for a normal, commercial 3/8 UNF nut.

You need something custom made then. A possible solution is to drill out a 5/16" nut with 9.5mm and rethreading it with 3/8unf.

Oh, I have a few of those already....