At my airport the grass cutters start work at 5am during the cutting season and work up to the edge only when NO traffic is departing or landing (regardless of type). They finish when the morning rush begins....
Our Grass is cut by contractors but they are very good on the Airfield and trusted. ATC would still not let them into the strip during operations...
Seems a bit odd at your place. What if Q400 or the like were operating? Are you saying that even then they work up to the edge????