So, what kind of hay are we talking about?

We have taken fields with heavy dogbane pressure, planted them to alfalfa, and wiped out the dogbane using no chemicals.  The dogbane cannot stand the frequent, 4-5 mowings per year that alfalfa gets. By the time the alfalfa stand is shot, the dogbane is gone.

With grass hay, where you may mow once or twice a year, I don't think that will work. Grass hay typically doesn't get mowed frequently enough to put pressure on the dogbane, and it has a chance to recover.

Pastureguard HL has dogbane on the label as a weed controlled. I have not tried it.