A little more judicious sanding with the sanding drum in the Dremel tool yielded a freely-turning turntable. Curiously, it turns freely about 30 times and then it seems to bind up again. I may have more sanding to do yet, but I decided to move on to the next step.
While I still had the top on, I marked its centre by clamping an arm across the centre and moving a pencil along the arm until I made a spiral that ended at a point. I then scribed a diameter and checked that both ends align perfectly when the table turns through 180 degrees.
The next step on the turntable will be to solder the “rails” on. These are 24 gauge nickel silver strips, as explained in my plan.