Your soil improvement efforts will be more effective if you think of garden soil as a living web of microorganisms, not an input-output system.
To minimize tillage, sow fall crops without pulling out the roots of the previous crop.
Fall-sown cover crops, such as winter rye, offer a hospitable habitat for beneficial fungi to live in over the winter.
Soil improvement is a matter of providing the right nutrients and letting nature take over. Using compost, mulching deeply, and limiting tilling will nurture the microorganisms — such has root fungi — that make garden soil productive.