Dump truck shaking, only when loaded

Hello everyone, seeing if anyone can point me in the right direction towards diagnosing this shake issue with my dump truck, which is driving me nuts.

Truck is a 06 International 4400 single axle, 7spd with 65k miles. I've had it for about 4 months, I use it for hauling dirt/rock/sand and occasionaly towing an excavator.

It has a pretty good shake to it, enough to shake things off dash and vibrate the mirrors. It only does this when loaded with 8-10 tons, and only between 50-60mph. 55-60 is about its top speed. It feels like a back to front/front to back type shake, maybe a little up and down. I can feel it in the seat, the steering wheel does not shake side to side. I cannot feel it through the shifter, and it does it accelerating, decelerating, and in neutral.
I can count the shakes, and they seem to come in "waves", shake shake shake shake shake, slight pause, comes again and again till I drop below 50. Hopefully I described that well, lol.

What I have checked/tried:
Everything under the front end seems tight. Bearings, king pins, tie rods, leaf spring bushings.
New shocks on front - no difference.
Front tires are new Toyo M170 11r22.5s. I put them on when I first got the truck.
Cab mounts look fine.
Motor mounts look fine.
New Spicer U-joint behind trans, and Spicer carrier bearing. Old ones of both had a tiny amount of play - no change.
The other two U-joints are tight. Driveshafts do not appear to be missing any weights. Do not appear dented/damaged.
Rear leafs all look good, no cracks.
Rear leaf bushings look fine.
Truck does not have rear shocks.
Rear tires are 295 75 22.5 Ironhead IDR 311s that the previous owner put on a year ago. With the truck jacked up and running in gear, I did not see them being out of round or any major runout issues.
The tread on all 4 of them, if you run your hand accross, feels like cupping (each tread block is taller in front, shorter in back). Not sure if that matters but they are wearing weird.

Hopefully I provided as much detail as I can, not really sure what to look for/replace next. Maybe rear tires?

Thanks

 

The tire shop said they checked for balance, however there are no weights on fronts.

I have only hauled the excavator a few times, I do not have electric brakes hooked up yet.

It has leaf springs all around, no airbags.

 

Thanks guys. When I did the front U-joint and took off the front shaft, I marked the splines and put it back how it was. It appears to be in phase. Does it matter if the U-joint cap part of the Yokes are in the same spot front and rear? I attached pics.

I also jacked it up again and took a video of the driveshaft spinning. Slight wobble it looks like? Hopefully video uploads.