I am normally highly in favor of aeration. In this particular case, with the pond so shallow and being in the north, I would definitely bite the bullet. Pump it dry, kill it. Pay the 2 grand to have it cleaned out and deepened, and a berm built up. You will be much happier with it. Then in a few years when the fish get larger and vegetation starts growing, get a small aeration system.
I was in a similar situation, but my pond was deeper, I was in the south, and I had decent fish in it. I wish I had pulled the plug 2 yrs. earlier.