Most of your green manure crops are full sun things. I can't think of a one for shade.

I think if I were you I'd lay down cardboard or newspaper and cover it with mulch, compost, animal manure and let the plants suffocating underneath become the green manure. The covered plants rot, the cardboard rots and you have an easy bed without a lot of digging and work.

I have a small farm so manure is always here. I get some big cardboard boxes or paper feed sacks and cover them several inches (sometimes feet thick) in manure/compost. Lot of plants can go direct into not so aged horse manure with no ill effects. Not the stuff with bedding mixed but raked straight from around the animals toilet areas in the pasture. Bedding mix needs to age longer but works.

I don't know if buckwheat will winter kill in your area. It's kind of an interesting looking green manure crop. Gets heart shaped leaves and white flowers. Winter rye will live and hold the top soil. Advantage to winter wheat and rye is they don't spread by rhizomes and the seed heads are big so you can turn it before the seeding starts.

Just so much easier layering over cardboard and waiting a bit.