I discovered the root cause of all my towing issues. It's not the trailer, not the hitch, not the weight distribution, and not the setup. It's the truck, and I am not very happy at all about it either.
I went to the feed store and got horse supplies which weighed very close to the weight when towing, and I specifically loaded it in such a way to mimic the weight distribution when towing. I had 480 pounds on the axle and slightly ahead of it, and 640 pounds behind it.
The truck drove just like it does when towing, the front is all over the place, left, right, up and down. It isn't as strong as when towing because the trailer amplifies it. I have my doubts that even the best hitch will resolve it. Am not happy at all.