You are correct, the w.mill is a whole lot better than no aeration at all. I've seen windmill aerators produce complete summer mixing in some ponds and not others. Several things affect the degree of mixing. It is possible that windmill mixing under the ice could throughly mix the pond especially if it is windy where the windmuil sits during the winter.
Since you are in west central OH is assume you got your w.mill from JL Becker. I would not trust much of what he says about fish & aeration unless he agrees to back fish deaths up with replacments. He is a contractor by trade not a fisheries person or someone with a biology background. He deals with heresay, stories, opinions and tests verifies little if anything about ponds.
Q1. Is your diffuser the 6" dia stone or a 10" dia rubber membrane? Membrane will mix at least twice more water per hour.
In central OH, move your diffuser shallower around Halloween or in early November. Replace it to deep water no later than May 20, but better in mid to late April or first week of May.
If your pond is deep +12', (which it is) not old and fairly clean bottomed (sludge and weedy) and you keep 1 & or 2 week old snow off 25% of the ice you do not need to run the aerator. winter running can cause mechanical problems if the diffser check valve is not working properly.
Q2. Do you have a presure relief valve in the airline?