I wonder if spraying with roundup right after you baled it and alfalfa had new growth would knock out the buckhorn but not affect the alfalfa? I haven't personally tried it but have heard it mentioned a couple of times.  If you plan to destroy it anyway might be worth a shot. I'm new to the alfalfa world so take my suggestion lightly.  My first year was kind of a struggle but second year has been going well. So far I have enjoyed growing alfalfa for a lot to learn vs row crops.