I do not have the S model but I do use a 12' Bush hog behind mine. I usually mow my parents vacant land with it once or twice a year. I mowed just about all of it in 9th gear.
We have sold 4 to 5 tractors with 15' batwing with no problem
I deliver 1 in the Fall he cut a Field that has not been cut for 2 years with no problem. Some of it was over Tractor wheels