We have a 07 20' Safari towed with a 06 Tundra (lighter load capacity than yours, but very comfortable ride).
Our dealer installed the 10,000/1,000 Equal-I-Zer correctly as instructed by the hitch mfg. On smooth highway it is fine, but on rough highway it rides terrible. Porpoising, pitching back and forth between vehicle trailer, extremely stiff. One rivet came undone inside and a/c vent covers and two light covers came off.
I loosened the weight distribution bars one bolt hole, the level of the truck still measured close to spec, and the next trip of 2,000 miles was smooth and steady, and the steering felt firm. I then returned it to original settings for safety concerns, even though I sensed no problems.
There is no way I would advise doing this however, because loosening the bars removes at least some steering control, and much more importantly, the extremely important sway control feature is compromised, maybe even lost! No way to know.
We love traveling with our 20' Safari, and safety is everything out on the open road. For that reason, after returning home, we will buy a ProPride hitch. Big dollars but worth it in emergency handling conditions.
My reasoning is its stellar handing characteristics, always knowing you have no trailer sway, and the ability to select and adjust the weight distribution bars to the tow vehicle you have, without concern for loosing sway control.
From the standpoint of towing capacity and payload, your trailer and new Tundra look like an excellent match, to me, others will disagree I'm sure. Some jealousy here of the new Tundra.