Not sure I would remove the rear drive shaft and start it up then put it in gear. If you do you will have a mess on your hands! The only thing keeping the fluid in, is the seal around the yoke!
When I pulled my drive shaft and the rear end was lower trans fluid came out. You can pull the front shaft if the vibration goes away you found the problem, if it does not then it's the rear shaft carrier bearing as you said the u-joints have been replaced. Not sure why a shop would replace u-joints and not the CB but I sure would not.
The transfer case in the Ram does not have any known issues so I doubt that is the problem.
Don