I don't know about the slippage but the "clunk" going from R to D and down shift is the bushings, very common.
I purchased all the parts from the dealer, they are online but shipping made the cost a wash. You will need two bushings and one mount bracket. I changed all of mine. The job is difficult but straight forward. I did it in my garage, it took me about 8 hours by myself. I only raised the driver side with a jack, and of course use jack stands for safety before ever getting under a raised vehicle. Take off the skid plate, if you have one, remove the front drive shaft, mark it before removal so it goes in the way it came out. Support the differential with a small jack remove the 2 bolts on the bushings first and lastly the mounting bracket. The top bolt is very difficult to get to, so be ready to come up with some ways to get to it. I used a 3/8 drive and deep well socket with universal. Lower the diff so that it is supported by the cv drive shafts against the lower control arms, now remove the sensor plug on top of the diff to avoid damage. Use an air chisel to remove the side and top bushings, use a ball joint tool to press in the new ones. It was difficult without a lift due to fatigue to my arms, I had to take lots of breaks. Just be patient and it will come together.