The Tow/Haul I'm familiar with allows the Five-Speed TorqShift to use all its gearing, including Top/Overdrive. Ford's since gone to a Six Speed with "Double Overdrive." From what I've read, they had to go UP (to a higher number) in axle ratio to take advantage of it. That might mean the new T/H feature keeps the Six-Speed out of Sixth. I simply don't know enough to comment.
I CAN say, the "OD OFF" feature is what 4R100 (came out with the V10 and was replaced with TorqShift around 2005) and the prior E4OD (1992-96 with 7.5L/460) used. In those, OD Off rendered it a three-speed, non-overdrive, function.
suprz is right. A Class C ***IS*** hauling, all the time. Our GVWR is 14050 like his, shipped new at around 11300, and we go camping at around 13800. That's hauling.
@suprz, You should have a label inside, probably inside a cabinet door, saying what your 31SS weighed at, leaving the factory. Ours is under the kitchen sink, but it seems they can be pretty much anywhere. That'll tell you what you can carry: 14050 minus that as-built weight. I'd like to know what that number is, for a 31SS