Good, so slippage is our only enemy (A.) because it elongates the arc (rather unpredictably) and (B.) because it strains the tower.
Perfect pivoting produces perfect positioning.

And the thing is, contrary to my previous worrying about the roughness of the stone, it's only one small spot on the stone that should affect the motion, i.e. the point in contact with the edge of the tower.

I think the Beeb man talked about making a notch, but rejected it on the grounds the ancients didn't.

So our only way to minimize slippage is to maximize turning speed? (subject to depositing the stone vertical of course)?