Over the years, I have owned probably three dozen Southern bags. Some were obviously home made, some were shop made. Most I have owned were probably mid or even late 19th century, but some I believe to be early 19th century or even late 18th century. If there was a provision for adjustment of the strap, the overwhelming choice was an iron buckle. Some buckles were crude and home made, a few were finely made and one or two even had a roller.
I just looked at the eight bags I still have which I believe are Southern. Five have iron buckles and three have no provision for adjustment of the strap. That is not, of course, a representative sample as over the years I probably have held on to those I found most pleasing. Shapes and sizes range all over the place. Straps range from less than 1/2" wide to over 2 1/2" wide.
When considering what is "appropriate" for a Southern bag, whether adjustment device, size and material for the strap, bag material, shape or size, I'd just observe that the old boys made them from whatever they had handy and did whatever pleased them. The bags were as individualistic as the owners.
Wayne