i think rear irs susp toeing on hard acceleration and as the tires slip a little and unload the susp unrravels on that side and back and forth you go.
i had this happen on my bucket with soft rear leaf springs(last leaf removed), i watched the susp and rear axle move forward and back unevenly as the tires grabbed and the springs wound up. i stopped it with a set of long homemade slapper bars and putting the leaf back in.
your case is a little different with irs ,any way to firm up the front rear movement of the rear would help. it may look solid but you would be surprised what torque will do.