First and hardest thing you have to determine is what part the noise is truely coming from, and listening from the cab is very unreliable. Good mechanic's will use three or four small magnetic microphones located underthere to narrow down the location quickly.

 

Following

 

U-joint would be my first suspect.
When was the last time you changed your front diff fluid. Drain and fill and check the plug magnet for chunks.

 

Similar gear whine issue but from rear differential though

Bought used with 160K miles (2012 4.0 RWD) otherwise in excellent condition

The noise was coming between 35 to 60 mph speeds . Took it to my mechanic for differential service and the noise level now has come down significantly also it occurs between 50-60 miles

My mechanic told me the the differential fluid appeared to be contaminated with water and I he recommended that i do a differential rebuild if the noise bothers me

i am looking for a salvaged part rather than a rebuild

 

Quick update,

Finally got the chance to put the truck on a lift, spin the wheels in 4WD to look and listen.

We didn't find much, yes I used few 'listening' devices and yes there's more noise coming from the front passenger side.

I replaced the front diff fluid and it was crystal clear, even though few years old. Not a single flake of anything.

One thing we did notice is that the driver side axle had a runout, visible runout of roughly 1/4".

I don't know if this seemingly bad axle is what causes the noise and vibration, it's a possibility.

At this point I'm more looking to replace this truck rather than fix it.

Thanks everyone, I will update more when possible.