A worn auger will allow grain to pinch or wedge between the flighting and the housing. A new auger will move the grain without the pinching, using less power.
How did you determine that it is the cross auger chain? Did you physically watch it jump a couple times? Just asking is all.
Can you turn the whole unload system by hand quite easily? If not, may be a bearing out. ? Remove the cross auger chain and try again.
There are 2 pipe braces like the one in this picture. One on the front and one on the rear of the boot. I've found the bolts both sheared, and vibrated out on these braces which allows the whole boot to move around.