A trip over it with a spring tooth wouldn't really be farming in my opinion. I wouldn't consider you a farmer and visualize you in bib overalls wearing a beat-up straw hat while knawing on a big piece of straw and hear banjos and washboards unless you confessed and bragged of such.
If you have a 4 wheeler you can buy a toothed drag for less than $300 and that would work for your size field. Aeration does wonders. I was reading an article about
@Nicky where she touted success with their meadows using aeration, overseeding and fertilizing. I know from the Colorado ranch where I grew up that had clay soil, our pastures, and hayfields got a good spring toothing every spring and sometimes in the fall. Ok, I promise to shut up about it now hahaha!