Thinking about how stones are flat on one side makes me wonder how the bi-convex form came about. It is lot of trouble to make that shape. It is much easier with all these materials to make something more like backgammon pieces.
We are not the first to ask these questions, leaving me to wonder where the rigorously scholarly and peer reviewed research is hiding. It is also fun to speculate wildly.
Disks are far simpler to manufacture from cylinders of many different substances from wooden dowels to delrin, from clay to plastics. The point in time When craftsmen started to cut disks from slabs of stone suggests a new development in tools and the use of abrasives, not just to polish but to cut. Sophisticated stuff. Molten glass requires a different type of toolmaking and refractory processes, perhaps adapted from the established crafts of forging and casting of metals.
I have photos of seen ancient Japanese go stones that have swallows and doves engraved or painted onto them. They appear to be biconvex. I am guessing that some random go stone maker, perhaps employed at a royal court, who also played go, undercut some of his disks and found them easier to pick up.
Clamshells are an obvious choice but black slate is a bit of of a conceptual reach because the two sources of materials are so far apart and the manufacturing requires different tools. That is, cutting and shaping slate is quite different from cutting and shaping shells.
I’ve done lapidary work with various rocks and minerals. I have been a woodworker. and i have worked with clays and hot glass. I would much rather pay any price for well executed go stones than ever attempt to make my own!