Hate seeing a question go unanswered so a little advice. Repost here on the TJ tech page and see if they can help. Also your video didn't post for some reason.
Your description of the problem does point to driveline issue at the rear. Could be u-joints or inside the rear end itself. Best i got so far.
89YJ 2.5L TBI, AX-5, NP231 SYE, Ford 8.8, Yukon Grizzly, Tom Woods Shaft, 33" BFG T/As, 4" lift, Warn VR10000s.
[COLOR="Blue"][B]AF Jeep Club Tail #184[/B][/COLOR]