Mike - a man of few words, but important ones.
I too use a sharp pointed pencil to draw around the inlay, then using sharp thin chisels, I cut INSIDE the lines. I use a very fine pointed knife to surgically remove the wood where it is too tight, indicated by the transfer of inletting black.
The pictures following are of a first rifle built in my shop by a friend. It is a TOW kit, I think, as the wood was not up to Chambers' quality. Harder wood would have yielded more precision. The two chisels you see used here are a 1/8" wide flat made from bandsaw steel, and an ancient 1/4" gouge, which I see could have used some sharpening.
First thing to do, after you're ready with stock prep, is to locate the position and screw it down to the stock. Now you can trace the outline with certainty. Remove the inlay, cut inside the lines, stabbing in full depth. Cut a relief on the inside of the inlet, and then remove the ground with a gouge across the grain, cutting toward the centre - never toward the edge. Apply black transfer, screw it down again, remove it and pare away where it is too tight.
Again, this is his first effort, and he did fairly well, I'd say.
This is the same Isaac Haines box you have illustrated. If there is a secret or key, it's patience, sharp chisels, and patience. Patience helps.