I had something very similar. Stock 20 hankooks. Dealer balanced and rebalanced, checked alignment. Dealer would do something say it’s fixed I would take the truck away and vibration was still there.
Anyway after doing this 3 times they replaced all 4 tires under warranty. Smooth as butter since.
22 PB here. If the roads have snow the trunk is in 4A or 4H mode and normal driving mode.
Never experienced that rear end lock up, also no bed ballast.
I find even towing a Seadoo in normal mode with a PB messes up the transmission after unhooking the Seadoo, the shift points are all off and not smooth.
I prefer using towing mode for anything towing, and when you go back to normal mode with nothing in tow everything is still smooth.