Vibration when accelerating up hills
I have a 2015 F150 3.5 Ecoboost xlt 5.5ft bed. Truck has 102,000 miles. Currently I have a bad vibration coming from what seems to be the transfer case area of the truck. I get it occasionally when going down the highway on flat ground but that's pretty rare. However when I am accelerating up a hill around 20-30mph I get the severe vibrations. It sounds like I'm running over rumble trips and I can feel it through my seat. If I let off the gas it seems to go away untill I try pushing the petal again. If anyone can help me diagnose this I would really appreciate it. So far I have removed the drive shaft and checked both u joints and slip yoke and it all seems good. I have also drilled a 1/16 inch hole in the innercooler and drained some oil out not much. Then I changed all plugs and transfer case fluid. None of these have seemed to help. When I drained the transfer case fluid a small plastic piece came out about an inch long and tubular in shape. I'm wondering if my transfer case is going. Any help is greatly appreciated as always thank you.

