What I thought was going to be the most difficult part about this project—cutting the cavities inside the box so the lid and base would fit snugly around the stone and line up with one another—turned out to be very easy.
I left the two pieces of cocobolo oversized in length and a little in width and used a trick that Bess Naylor showed me when building a frame and panel, where the stiles are intentionally left long and trimmed after glue-up: strike a center mark on the two stiles, align and clamp them together, and measure outwards from the center mark (rather than measuring from the ends) to make your layout lines.
Once the recesses were cut for a snug fit, I sandwiched the stone between the boards and trimmed them to length at the miter saw. The stone kept the two pieces aligned while I planed and sanded the ends and sides.
Clamping sandpaper to my table saw and sliding the box across it was a fast way to square the lid and base, and flatten the inside surfaces of the box.
After sanding to 400 grit, I wiped one of the boards off on my jeans and discovered a curious thing—it polished the wood. So I tried a piece of leather to see what would happen. It polished it even more, to a buffed sheen. The leather also gently rounded the sharp edges of the box. If you've worked with cocobolo, you know how sharp those edges can be.
There is no finish on the box itself, only the carved portion (with spray poly). I thought that finish might adversely affect the stone, plus cocobolo is an oily, dense wood and is naturally beautiful.
After spending so many hours on this little project, I can only imagine the the original was made by someone who really appreciated his oilstone. Not surprising, considering the close relationship woodworkers had with their tools in past centuries.
Nice to know that some things never change.