I wonder if using dried molasses on your lawn might help the microbes break down the grass clippings easier. DD in SE MI has very thick lawn grass in the sunny parts. She lives in an old remodeled farmhouse. Once summer comes, you can't dig in her yard. In the shady parts, it's all maple trees and grass is very thin and the ground hard with all of the tree roots. I have silt over clay here and we only bag in the fall when the oak leaves start falling. We do leave some shredded leaves for the lawn but not too many. You might want to look into either raised beds or hugel beds for veggies. Reid did a really neat job on a raised hugel bed.