I should have added that the outer diameter of the counterbore for the screws is right on the edge of my playing area. In other words, if I take a straightedge, stand it vertical, and place it lightly against the edge of the cushion, the straightedge comes right to the edge of the counterbore. That's why I'm glad you mentioned the compression effect of the ball and the fact that over time the balls will probably cut the cloth around the counterbore if I don't fill them.
The counterbores are 1/2" to 5/8" diameter. Will such a large area of beeswax eventually soak through and stain the cloth? If not beeswax, then what would you recommend so that the next time the table has to be taken apart, it won't be so difficult?
Thanks for all your answers and helpful information.