Doug Miller writes:

No. You confuse temperature and heat. The phase change is crucial.

Well, yes, but so is lowering the temperature at which that phase
transition occurs.

The retention of melt water is a spoiler at any temperature. The product
must be in continuous, intimate thermal contact with the unmelted ice, and
the melt water rapidly drained away. This is what makes the heat transfer
fast. Undrained, the heat transfer slows down remarkably. The melt water
has no appreciable heat-sinking capacity, and just interferes with the heat
leaving the beverage and flowing to the ice. And the OPs desire was for
the fastest possible chill. Using brine (or glycol antifreeze if you
really want to experiment) will also lower the terminal temperature,
although it slows down reaching it, to where the beverage will be frozen
and slushy, not good.