Mulches work. Today my buddy, our wives and I shovelled up 20 cubic metres of wood chip from a tree extraction site. Hot sweaty work. My half will go on the gooseberry bed 6" thick. Over three years it will rot to nothing (suppressing weeds for three years). I have done this for five years on our herb bed, never dug it. The soil is like fruit cake - dark, rich, soft, fertile.
Good old horse muck works too. The new neighbours the four of us sorted thirty trees for are horse trainers who were wondering how to get rid of the manure. We solved that problem for them
We have put several inches of manure on our veg beds for years in the Autumn - rotovating it in for spring. I'm amazed how much the soil can take - but it pays dividends for sure.
If you do want to go green manure - try clover - great, fast growing, nitrogen fixing, ground covering, simple to turn in.