I think soil testing and remediating by what you find would improve the soil a lot. By no means resort to chemicals, but simply adding the minerals missing would help. I'd suggest Logan Labs for the test and use the worksheet from The Intelligent Gardener for the mix.
I picked up a bunch of soil test kits a while back. I have a microscope and a minor chemistry lab to test my dirt. The land is calcium and iron bound. Really high in iron. The plan is a series of different cover crops and some animal rotations over the pasture/fields. It will take some time, but they will improve. The potash will help with the calcium deficit until the soils start to let go of what's there already. It might sound odd, but I would actually smile pretty big if the dandelions suddenly took off across my front field. Nature's little vitamin pumps, those.