After going through a bunch of leather NATO straps I've decided to put an HD alligator on my Sub and leave it.
I've come to the conclusion that leather NATO straps just don't work. The thick ones look ridiculous, and won't work on many watches, certainly not a Sub. I must say it does not work very well for the Seamaster above either. Meanwhile, Leather thin enough for a decent looking NATO strap simply won't last over time.