Dave, I have done coarse checkering in the past, at 10 lpi. I did use a checkering tool, a 90 degree cutter, but left the tops flat. I can well imagine how much crisper it would have been if I had used something like a slim X-Acto modeling saw - I think it would have been a lot truer on the 1873 firearm I was working on.
And every time that I have done checkering, I have done it on a finished firearm. When the job was complete, I would use an old tooth brush and brush finish into the checkering.
But on these beautiful longrifles, I have been wondering about the stain, and if you are going to be using AF, for example, how one might protect the existing finish around the checkered area. Masking tape? Really don't know.
I do know that checkering on raw wood is very difficult, with tear-outs and such. The finish makes the surface of the wood much more durable, and easier to stand up to the cutter, be it a checkering tool or a saw.
Maybe you have a tenon saw, or something with very fine teeth that you might experiment with. Let me know how it goes, so "I" don't have to be the experimenter!