By short term do you mean just 1 yr? I plant oats to harvest underseeded with Alfalfa /clover mixture and use a Sunflower soil finisher and work it down in the spring with the 1st pass at 8-10" tall and about 2 wks later run finisher over it again and had probably 98% termination. If your hay stand is couple yrs old it will be harder to terminate. 

I personally would plan on letting it grow to at least 8" tall in the spring and get the benefits of "Green Manure" and do it in several passes at least 10 days apart. Maybe it would take 2 passes on the 1st day to pretty much cut the roots all off. I really don't know what kind of a job a Lemken does but wouldn't mind finding out!