Update 3

Based on amu1986's very helpful comment below, I've worked on a theoretical model for how a belt button could work.  The "button" part is actually the base of an upside-down button stud.  Since I'm pretty sure there was no such thing as screw threading, it would be attached by rivets in the form of additional stems.

These buttons would have to be custom cast for us.  As a cost-saver, I suppose it might be possible to use a screw-back concho with a longer screw, clamping the concho to the outer belt layer with a square nut and reshaping the screw to act as the stud.