Chris writes:

For water, the heat of fusion is about 80 times specific heat...

So -70 C ice would have almost twice the cooling effect
as the same amount of barely frozen ice, right?

No, because heat load is proportional to temperature differential.

Now if you put that supercooled ice into watery payload that freezes, then
the supercooling heat sink will convert to new ice in the payload, and a
different process is involved that is more "efficient". However, this is
no better than just freezing your food to start with.

Hardly anybody appreciates that temperature and heat are two different
things.