Just some thoughts, but whatever you can do to get some specific training should help. Toss the keg as often as you can, even a little every day would be good.
If you can't get an actual tire to train with, shouldering a sandbag might be good. Lifting things with your knuckles scraping the ground takes getting used to.
For the truck pull, you could buy a couple long tow straps and pull a vehicle around. Apply the parking brake a little to get some more resistance. (Apply it a lot if the car is a Cooper.) Experiment with different shoes, traction makes a big difference with heavy dragging.