Back when I had an 8 acre pond down south, my aeration system used 6 diffusers. In winter there was rarely any ice cover, but I would turn off the deepest 2 diffusers to reduce cold water stress on the fish.

My new pond up north is only 4 feet deep. If I don't run a diffuser in winter I'm concerned about low DO under ice cover. If I do run a diffuser in winter, I'm concerned about low temperatures at the bottom of the pond.

Is there a way to limit ice cover without reducing bottom temperatures in a very shallow pond?

In winter, I only run one diffuser, and in the shallower area, (Wisconsin weather).
If I had your dilemma, I'd probably incorporate a timer. Not sure how often you run up north to the pond, but I'd turn it off completely during any sub-zero cold snaps then resume timer operation for mild winter weeks.

Here in Michigan I keep my diffuser running 24/7 in the winter at 2-3 feet deep next to my dock,my other two diffusers I close off. One it keeps the ice away from the dock and two it does add DO without chilling down the rest of the pond. After 5 years I have had very little winter kill, just a few fish and it seems to work for me, hope this helps.