Jim, i'm really far from being an expert. I'm moving my steps in the never ending journey of learning...
About your questions, well... yes, we have many example of stamped rings with religious meaning, names, etc. but it was mostly done in the islamic areas of the world.
I do personally never seen any "contruction marks" in specific sections of mail pieces, mostly because mail armors were not designed to be "taken apart" and put back together. When you needed to redo it or modify it, you did it by "cutting and sewing" the new piece. At least you can always add some marking rings just clipping them on the others and take them off when the work is done.
The rusting problem is another interesting matter. We know by experience that the most you use your mail armor, the most it kept clean by itself, just thanks to the movements the rings makes.
The problem comes out when you don't use it so often
But of course, i can image that wearing a piece of metal in the middle of the jungle and keep it "safe" is an hard challenge for everyone. I don't know anything specific on this topic, but i do know what indians used to do for keeping their Zirah Baktar protected by rust (the typical indian mail armors)... they covered them with mud, and that why we often see armor from those regions coming out with a relative brown color and stain overall.
Maybe they used to do it also in the middle of the New World?