Hi,
I've made, sculpted, polished, and engraved many of these kind of side plates.
First, clean up all the edges with needle files. A half round file will be your most valuable shape. If you have a jeweler's saw, use it to get into the tight spots along the edges. Then the plate needs the surface casting texture removed. File that down with small needle files, and sanding sticks. Sanding sticks have a spring loaded mechanism that holds a thin sanding belt. You can get them from most wood working suppliers. Then you will need some polishing stones, like the Gessweins that James mentioned lubricated with lamp oil. Also of value are hardwood sticks shaped into pencil points that can be dipped in lamp oil and rottenstone, and then rubbed on the metal to polish it. Once the textured surface is smoothed, you can really polish it with 3-M bristle discs in a Dremel tool. The discs are readily available at online jewelry suppliers. Unfortunately, you may lose some of the sharpness of the edges of the design during that process. They get sanded down. The only good way to recover those sharp features is to engrave them after polishing. You have to remember that these kinds of side plates were made by specialist with training you don't have.
To be honest, these plates give me no heartburn anymore when inletting them. I fabricated this scribing and stabbing in knife, which makes the job easier.
These micro chisels are also invaluable for stabbing in the outline
Just go slow and make sure your chisels are razor sharp. In addition, the mortises for these side plates was very shallow. So don't cut deeply.
Good luck.
dave