Rear end all over the place??

[Houston Ben]

Hi all,
I have an 86 C10 with a 2011 5.3 W.6L80 behind it. After the install of the 5.3 my rear end is all over the place. I installed some traction leafs to help with the axle wrap and it helped a lot but the side to side motions the rear end does when I get on it still scares me. One time I jammed on it to get around a vehicle and it almost pulled me into the vehicle.

I just installed a 2/4 Belltech drop with their SP shocks and the ride is much improved but still bad side to side movement. What can I do to stop this?

Thanks for any help, I am at a loss on this as I have no expertise in this department or any other for that matter.