Dump truck shaking, only when loaded

Alright, with the rain here lately I've had some time to mess with the truck a bit more.

1st test I did was mounted a Gopro, loaded the truck up and drove around at the magic speed. I mounted it in various spots underneath,outside, and by the driveshaft. Nothing too obvious in a few hrs of footage, but looked like the rear area of truck was shaking more.

Next experiment was to jack up the rear again, but this time run it up to 55mph.
Doing this I felt something shaking, although much less violent as when its loaded on the road. Looking closely at the tires while spinning, It appeared two of them were a bit out of round, with one also having side to side movement.

So I bought a spare used tire, balancing beads, spooned it on to replace the worst one and took it for a test run. No difference, bummer. Came home, swapped the 2nd worse one with the first tire, and no change as well.

What are the chances that the other two tires, although appear fine, could have a broken/separating belt? Not sure if that would cause more of a shake loaded down or not. I'm fine with replacing all but I'd hate to do that and not fix the issue lol