Yes, I understand that it is concave... my question is whether the text is reversed. The photo you posted above where you outlined the text makes it look like the text is right-facing, which would indicate that this isn't a mold or die in the traditional sense. It could still play some sort of role in the making of buttons, of course, and it might actually be some sort of "matrix" die (essentially a die for making other dies). I'm just trying to figure out exactly how it was supposed to work.
Regarding the clay, let me make a suggestion: Get some Sculpey brand polymer clay. This stuff is really good about not sticking to anything else other than itself, so you shouldn't have to worry about it sticking to your relic when you press it in. Take a BIG hunk of it, much bigger than would fit into the depression, and push it against the cavity. Heck, form the stuff into a handle for yourself and just push the end in. If you want to be extra-careful about the clay not sticking, mist the relic with water first. Sculpey is designed for using in push-molds, which is essentially how you will be using it.
If the impression comes out good, you can bake the clay in your oven at 175 degrees and have a permanent impression.
You can get Sculpey at any art supply store.