First do you have a lathe or access to one.
Chuck the big end up center on the ball on top of the finial and drill say 3 in. down then make you a piece that would be the same size as the small ball cut it in 4 pieces put on ball and clamp in a chuck. find the center on the bottom hold in place while tightening with live center and drill from the bottom to meet the hole previously drilled. If you have the centers correct then the hole will be perfectly centered.
You could do one on all of them at one time and then the same for the other end.