Right! So! Uhmmm... I changed the t-case oil - no more slipping, no more shudder. I'm happy.
The old oil was filthy so I flushed it completely with a quart of fluid before filling it.
So if your truck is slipping in tight turns at all times, forward or reverse, in 2 or 4 wheel drive - REPLACE YOUR T-CASE OIL. It's easy, I did it on my lunch break.
And while at it, service your front and rear differentials!
P.S. I used Valvoline ATF fluid to fill the t-case and although it stopped the slipage/shudder the noisy whine continues. Can someone recommend a fluid that better deals with the whine?
It sounds /exactly/ like it sounds when it's in 4lo...