We are having kind of the same problem at our field and the only thing that may help you is to take moth balles and drop them in the holes and cover up this will drive the varmonts out of the field and into the taller grass if you stay on top of it and do this every time a hole appears eventually this will give them the idea to move to the tall grass. They should after a while stay off the field and you should not have the problem after a flying season
