Thank you for the inquiry. The question of "final polish" has been around for a long time. Basically, the technology remained largely unchanged until recently during the modern Callenelle iterations. The final polishing process used by ABB Co. was quite basic.
Please allow me to begin at the beginning. As you know, the early ivory ball blanks were extracted from tusks with various manifestations of core bits or saws. Once the blank was turned, cured, turned again (and again if needed) the ball was polished on various buffing belts and cotton buffing wheels by hand. Because of the natural variation found in living things, achieving exact accuracy of diameter and weight was not possible with ivory. With the advent of composition balls, the process remained roughly the same, with final polish done by hand.
When phenolic resin balls hit the market, the molding process became much more accurate, thus the finish lathe turning phase was greatly shortened. There was an attempt to automate the process at that time. I don't know anything about that and I have not been able to locate the patents which would describe the equipment. Hand turning was accurate enough because the lathe jigs were fabricated to assure replicability. The key, however, to diameter uniformity was the development of "centerless grinding." Centerless grinding ultimately brought the balls into near perfect roundness while also smoothing the surface almost to the point of being "polished." Modern grinders can polish to perfection. At ABB Co., operators took the balls from the centerless grinder directly to the buffing line where the balls were brought to the final finish, boxed and shipped. There were operators there who bragged about being able to buff better than any computer ever made.
(below, a picture of a simple modern centerless grinder/polisher)