A CAD program could easily determine where receiving holes would be on the top surface. A forstner bit would allow drilling without drilling through.
The problem would be alignment. With so many dowels, and they are not parallel, you would have to feed them one at a time through the bottom to the top surface. Gluing that would get sloppy, probably not much better than the current epoxy.
And to be honest, I would question the holding power of the epoxy on the end grain. But the fact that there are so many points of contact, it’s probably fine.