. . . could also help, Anthony, because the holes will be punched in a different location. It doesn't take much of a shift to produce a fit that will remain centered on a wearer's wrist.
The closer one gets to an optimally placed hole and the more supple the leather, the greater the likelihood of attaining a proper fit. I'm having this very problem now with my Grand Seiko: the supplied strap is fairly stiff, and the hole that fits best is on the loose side, so it 'rides' all the time. I've got to find a better fitting strap.
Art