I use Russian Comfrey, Bocking 14, for all sorts of things:- mulch, incorporating in the soil under tomatoes and chillies, liquid plant food, on the compost heap, attracting and feeding bumble bees, animal feeding........
However, you're right, comfrey is not a green manure, and if you were to plough in the roots, you would spread the stuff all over your veg area. I'm not sure what you mean by a 'mucky plant', but if you mean it pops up everywhere from root sections (doesn't seed) then yes. I grow it just the other side of some fences so the sheep can nibble the leaves but not destroy the plant. I also have a large patch which I allow to flower for the bees, but if I'm late chopping it down and composting it after that, then it can be a bit messy, as the flower stems fall flat. You can cut it 4 times a year and still keep it growing.
For overwintering green manures, grazing rye produces a lot of bulk, and should be fairly cheap to buy. We left ours a bit too long, because we wanted to see how tall it would grow (over 6'
) and to produce a grain crop. By then it was almost impossible to chop the roots, so the lesson learned was to chop it down when about 6" tall, allow to wilt, then turn it in.
For raising the nutritional levels of your soil by the use of green manure, what about field beans (coarse broad beans grown for animal feed), brassicas (any, including grazing rape), agricultural lupins which bring nutrients up from very deep down? Also, mix in any left over vegetable seeds with your overall mix, such as peas, garden brassicas, sunflowers (bird seed), even lettuce. Whatever you choose, you want bulk, and to think about the nutrients each plant will bring.
If you don't let the green manure get too tall, then once it has grown to a few inches high in early spring, chop it down then plough it in. Leave a couple of weeks before sowing seed, as the initial breakdown process robs nitrogen from the soil for a while, before returning it. Established plants can go in straight away.
The benefits of green manure include protecting the soil, especially over winter, adding bulky humus, adding various nutrients to the soil, improving soil texture and suppressing the weeds.