Thanks for this article. That's a pleasant way to make our brains running a bit.
Firstly, I would disconnect the convergence of the duration and the object that Clarck and his friends build. Having a converging time does not mean necessary that the mathematical operation leads to a defined object.
If you are in the frame of the set theory with ZFC axioms, Clarck build an actual set of balls with the direct application of the axiom of choice : from an infinite collection of set of 10 balls 10n to 10n+9, you extract all the 10n. Bruce does not.