Update: After 15k miles, the vibration in my truck has been increasing gradually. I recently acquired another used transfer case to eliminate it as the source of the issue, confirming it's the new T-case was not the culprit. Despite replacing two rear drive shafts the issue does not seem to go away. However, if I rotate the driveshaft at the T-case of rear differential it will change the speed I get the vibration at. Driving without the rear drive shaft reduced the audible vibration significantly, but the truck still shakes at specific speeds (45, 55, 60, and around 70 mph).
Next step is to source a rear diff to rule out problems with rear diff.

Absolutely baffled! Can anyone explain why changing the transfer case would cause the rear differential to go out? I've been troubleshooting my truck's vibration issue for past couple of months. Any insights or advice would be greatly appreciated!