You said earlier that is did, which had me confused.

Show me where.

So, yeah, at point in time t, when the fluid being cooled has experienced delta T, the amount of energy pulled from it is the same, regardless of how long it took to get to delta T

But point in time t is variable and indeterminate, delta T is variable and indeterminate. THAT'S WHAT YOU'RE SOLVING FOR.

We know it didn't go into the glass or atmosphere, that would violate one of the LAWS of thermodynamics.

It would do no such thing. You're presuming the glass and atmosphere are perfect insulators, which would violate the laws of thermodynamics.

So, knowing that all of that heat energy went into the ice,

You know no such thing.

all we have to do is decide how it was distributed.

…and how it got there.

…and how long it took.

…and what the efficiency was.

…all of which are variable based on the geometry of your ice and the convection caused by it, which is - again - a variable you're attempting to solve for.

If any of the solid ice remain un-heated (from -10 to 0C), then the balance of the energy must have been removed by phase change or heating the water.

wat

So, does one large sphere warm more evenly than 4 small cubes?

Remember when I said I wouldn't model this with a ten foot pole? That statement has not changed veracity lo these many weeks.