[wdfifteen]

I wonder how many BTUs of energy would need to be extracted to effect the phase change if the ice was not doing work while the H2O restructured. I suspect fewer. It's been a long time since I studied physics and I don't have time to look it up right now, but I think the specific heat capacity of water would be lower if it did not physically expand (and do work) while changing phase.
Comparing it with a hypothetical substance that does not expand when changing phase.

BTUs to lower i gram of hypothetical substance 1 degree = X

BTUs to lower i gram of H2O 1 degree = 2X