I designed those flat discs so that they were just a hair bigger than my 3" jaws on my chuck. I would turn one side and the edge, then part it off. Place it in my chuck with a plywood spacer to move it out far enough and then turn the other side.
for the ornaments with finials I turned a sort of flat doorknob shape. Sanded and textured one side. Then center drilled it 1 1/8" all the way through. then I made a wooden expansion chuck to hold it to sand and texture the other side. Then I put it on the drill press and drilled through the sides to hold the finials. I made little chatter tool buttons to fill in the 1 1/8" holes.