However the % change in volume of any reasonable shape of water is so insignificant compared to the difference in energy of hot water and cold water that this e

However the % change in volume of any reasonable shape of water is so insignificant compared to the difference in energy of hot water and cold water that this effect is almost certainly negligible. You underestimate the energy the evaporating water takes away. The evaporation energy is much higher than the specific energy. The amount of water that evaporates is not only significant: it also causes the temperature to drop more sharply than you would expect based on only the larger temperature difference. When they reach the same temperature, there is less of the water that was hotter initially. As such, that body of water will be frozen earlier.