I think the point of case hardening, at least in the case of shotguns is to create a hardened outer shell to prevent wear, but to keep the inner layers unhardened to keep the forgings from cracking from repeated recoil. they were using steel forging processes to shape the parts.Nitriding and carburizing surfaces is easy. What is difficult is to get the stuff to penetrate deeply. That's why they used to pour charcoal on top of forgings and just hammer it in.
I don't really understand the process myself (or many other parts of metallurgy) but I suspect it may use heat as a relay system for carbon atoms to get in. In other words, to get the inner iron layers to "steal" carbon atoms from the surface, and repeat the process, until it gets to the core. Therefore, the central consideration in such process is not the chemical composition of the hardening compound, but the carefully controlled environment the work piece is kept in.
This has to be the closest call ever!!!!
the process is definitely a transfer of carbon, plus the quenching. I know that any engraving had to be done before case hardening.