Well the actual Edward Marshall buttplate has a couple little cuts that Jim Chambers' casting does not. I don't know whose casting you have, but that would just add to the challenge.
First prepare the buttplate well, with good uniform draft on all the top edges, and smooth transition from the top to the back.
You'll have to do some preliminary shaping of the wood on top to approximate the final shape for best results, but be careful not to get carried away.
I start by getting as good a fit on the back as possible, before starting to inlet the extension. The back of the Marshall plate is pretty flat, making this part a little easier. With a good soft casting you can always bend the back a little, later on, to close minor gaps.
Finally just start inletting the top like you would an inlay and take your time working it down slowly.
It's nerve racking and tedious for me, but my results on these type plates have generally been better than I first expected.
Good Luck!
Jeff