Truck shakes at 60+MPH

Check alignment?

 

If the truck is shaking but not the steering wheel, then I'd bet something on the driveshaft, like a u-joint. I had a bad steering wheel shake from bad upper and lower control arm ball joints and bad tie rods. Replacing those components eliminated the shake completely. I have a mild vibration at 20mph and 42-ish mph on my truck, but only when on the gas. 2.25" lift in the front, 1.5" AAL in the rear, needle bearing has been swapped out, so most signs would point to driveshaft/u-joints. It's not enough to get me to fix stuff just yet.

One more data point would be shifting to neutral at 60 or coasting down through the vibration range and seeing if the shake still happens without power from the engine and transmission.

 

Steel or aluminum wheels?
I went to steel wheels because of the condition of the OEM stock wheels. My experience with steel wheels has been to hand-tighten all six lugnuts to set the wheel before applying torque. Once I have them hand-tightened I work my way up to the 85 lb. ft. Example: I torque them all to 20, then 40, then, 60, and then 85. Something like that, it varies on my mode. Since I've been doing it this way I have not had any wheel/tire shake.