fwiw...
Have used buckwheat. Very popular with the venison. I planted late spring and then turned down what was left to plant a fall cold plot.
Grows quickly...I believe it pukes with the frost...but it doesn't matter, the deer wiped the majority out anyway.
When motivated, do disc in the rye/wheat in spring and buckwheat in fall, as green manure. Like field rye/winter wheat, it is relatively cheap--and I always add token amounts of the least expensive short clover to each.
