Well, yes I do rotate. I rotate my field crops too. I probably should try a cover crop. Do you recommend Rye?
Rye is a good cover crop. I plant winter rye in the space where I plan to plant corn in the spring. It needs to be worked into the soil several weeks before you plant the corn, or germination will be slowed.
Hairy Vetch and clover are also good cover crops. I also plant winter wheat in the fall, and in February sprinkle in some clover.
Yes , I recommend Rye The 'inoculated' is a nitrogen nodule fixator to the seed, which also provides nitrogen and fiber to the soil.
Thus it provides fiber to break up the soil and provide organic content , and nitrogen for the following crops.
But it must be broken up into small fibers via a lawnmower , or it will bind any roto-tiller
Also , consider dandelion, which breaks up the soil, and sends roots down to 15 feet that will bring up micro-nutrients to the topsoil.
Another is mustard seed, the yellow flowering 'weed(?)' which also brings micro-nutrients to the topsoil.