When is weight distribution needed?

So my thoughts are to drop it on the ball and try it... Am I nuts?

What weight are you trying to distribute? You have over 12,000 pounds capacity with the rear tires, more than 9000 pounds rear axle capacity, and why would you want to redistribute weight to the front of an already heavy front end truck and some (25%) back to the trailer tires? If the receiver hitch can handle the tongue weight why mess with weight distribution. Sway is another issue but your question is about weight distribution. And, yea, I also have a 3500 dually and a 31 foot travel trailer and on the ball works just fine as long as the receiver is up to the weight capacity.

Toyhaulers empty are typically nose heavy to compensate for the weight of the toys that are carried in the rear. Don't load you bike to far forward as that will only add more weight on the tongue that you probably don't need. If you have 10 percent or more of the total weight on the tongue you should not have a sway issue. 13 percent is about ideal.