The F-350 is certainly a bit of overkill in truck size for a travel trailer. You don't really need to distribute much weight to the front axle. If you are comfortable, then I would pretty much leave it alone.
Yes that 4,000 - 5,000 pounds on the rear axle of the F-350 will keep it planted in a curve or on a windy road. While the Nissan probably only had around 3,500 on the rear axle? This can allow the weight in the front of the trailer to keep it 'plowing forward' and push the rear axle in the way the trailer wants to go, not following the truck properly.
Make sure that your replacement truck tires stay steel sidewall, as the softer polyester sidewall tires can (and in the case of my motorhome do) allow the towed vehicle to push around the towing vehicle.
Happy camping!
Fred.