Yeti, yours sounds like the brake proportioning valve needs to be adjusted to account for the added distance from the rear axle to the frame. Either that or retorque your U-bolts, the axle could be shifting a bit as the binders go to work.
83srtoy, anything that is loose, or worn out will be more noticable under heavy acceleration. You are putting much more stress on the components when accelerating than just costing down the road. Think about riding a bike, when you first start up you are pedaling pretty hard. The force from your legs make the bike shift left and right. Think about all the pressure you are putting on the pedals, and therefore the chain. Now think about just gently rolling along on a straight street at a constant speed. Very little work needed from you to keep the speed, right?
Same thing goes with the rear axle on acceleration. The rotation of the driveshaft will turn the pinion gear which in turn causes the axles to rotate. I didn't really have to explain that, but all that force causes the rear diff to rotate a noticable amount, putting more stress and angles on the U-joint, and pinion. Just cause the driveshaft appears good when the truck is parked don't mean its still at that same angle during the heavy acceleration you are talking about.