It is unlikely that aerating your pond would reduce evaporation. In small laboratory tank experiments, aeration actually increases evaporation by putting more water in contact with air. In large reservoirs where the volume of water in the bubble columns is relatively small, there can be slightly decreased evaporation in the spring due to the effect you mentioned, but on average, the effect is negligible. Also, in order for the deeper water to be cool enough to make a significant difference, the pond would need to be about 18 meters deep. I am guessing that your pond is shallower.

Another detail you might want to consider to keep more water in your pond is what the bottom is made of. The finer grained the soil, the less water will soak into the ground. (On the other hand, as long as you have a well to get it back again, you might want to let all of your water soak into the ground, as it won't evaporate from there.)

Aeration is the process of infusing oxygen into the pond. It’s really important for growing good bacteria that eat all the nutrients in the water. This reduces much, increases water quality and clarity, and eliminates that yucky rotten egg smell. It’s also important for moving the colder, oxygen-deprived water from the bottom to the surface. Colder water molecules move slower and don’t escape the surface as quickly. Although it might not completely fix your problem, the water should evaporate a little slower!

Adding aerators to the pond will actually make it evaporate faster! By mixing the pond and bringing cold water to the surface, you will actually increase the rate heat is transferred into the pond, which will make it evaporate faster than if you did nothing. The rate that heat is transferred depends on the temperature difference between the two things that are in contact. In your case, the heat transfer depends on the temperature of the surface of the water and the temperature of the air. If you make the surface of the water colder, the heat transfer gets faster, and the pond won't last as long!

Keeping the surface of the lake colder would reduce the rate of evaporation and keep your pond drier. I do not know if aerators would help with that, though - aerators would generate heat just by their operation.

No, according to this: "Evaporation rates were found to increase with greater aeration rate."

Effects of mechanical aeration on evaporation rate and water