Impressive physics and chemistry by all.  Haven't taken any of it since HS,
but it was interesting.  I think I followed most of it, but to me, the
argument is like the theory of relativity.  Fine in theory, not in practice
(not to open a whole new can of worms).
    The one thing missing is something Kurt alluded to at the end of a long
explanation:  That there would be less ice in the end from the water that
was originally hot.
   This is not a point to take lightly.  You would need more water to
surface the ice, in this instance, and therefore lose the effect from the
hot water freezing faster.
 
  At least we can all agree on why hot water is used:  Because it helps to
combine with the old ice.
                             AW