The following approach is not for everyone.
You mention clods as the problem. Are these semi-chewed plants, roots and soil which the rototiller failed to break? If so you already have your organic matter! The trick is getting it submerged where it can break down over time and yield valuable nutrients and humus to your garden soil just as farmers plant and plow under cover crops such as clover, buckwheat, winter rye etc. Some of these have more immediately available Nitrogen than manure, others P and/or K. I have the same problem, even after several passes with my 14hp BCS tiller clods remain. I used to hope they would go away, but, they made lumps and holes in the black plastic IRT mulch and didn't decompose at the surface. I don't have a plow or harrows yet but hey there's that nice backhoe on my tractor. So I changed my garden plan to use long straight rows with clover borders. I dig a straight 200' row turning over each bucket carefully upside down back into the hole. I hand groom the row for rocks and the occassional archaeologic treasures. Then I rototill and mulch, ammend, and plant. I mow and blow the clover border back onto the row as needed.