I went back and re-read your post where you described what your feeling. That does sound like locker wiggle to me. Basically the truck is changing directions..
Soft rear springs and/or caster change via the front left lifting some when you get on the throttle can change the direction. Even different tire pressures will make it change direction.
The word "wiggle" can be misleading.. its not like the truck wiggles under you.. It changed direction and you correct it and viola, it wiggled.
~Mark