I vote for buckwheat. It is an amazing crop and wouldn't hurt the neighbors livestock. It's considered a superfood, too. I grow microgreens commercially and one of the ones I grow is buckwheat. The extensive
root system is makes is very impressive! I see why it would be considered green manure. The other wonderful thing about buckwheat is how hardy and non-finicky it is. I realize we are talking about completely different contexts, that is microgreens vs. growing large areas in one's garden,
yard, or acreage with it, but the buckwheat doesn't care if I seed it in acidic soil, alkaline soil, whether the air is a bit too hot, or a bit too cold, it grows, and grows well. And you can harvest it, too, and add it to salads, stir fries, smoothies, etc.. It has a very mild flavor, with just a touch of lemon flavor to it. It is also a complete protein, providing all 8 of the essential amino acids that our own bodies cannot manufacture on its own, and has other good things as well. It is not a wheat, of course, not even a true grain, but rather a pseudo-grain, same as amaranth and quinoa. Buckwheat is amazing!