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Don't slice the ice! Concentrate on warming the exposed metal tubes containing the coolant - Soon to be 'warmlant' - to defrost the deepest parts quicker.
And when storing the frozen food, cold air drops, so put the freezer bags into a plastic crate, creating a cold trap around the base for the cold air to pool into - and put most vulnerable food on bottom, and all sacrificial (ie ice cubes, freezer packs) on the very top!
I'm afraid physics can't help with with the printer.
Two things.