If for some reason (?) you wouldn't want to take either Tim or Pete up on their offers (which is good info to know, by the way), you could use threaded truss head rivets. These would look fine from the sides, but obviously incorrect from the inside where the nuts would show.
While on this ashtray subject, it was noted in the original Post that the ashtray was just recently zinc plated. IMO, my original pieces appear to have more of a Cad appearance than zinc. To me, these two finishes age differently, and mine seem to be more like CAD. Which is correct ? Were there Plant differences, or running changes ?
Bob